CAMERON UNIVERSITY

DEPARTMENT OF MATHEMATICAL  SCIENCES

LAWTON, OKLAHOMA 73505-6377, USA

 

CURRICULUM VITAE

IOANNIS KONSTANTINOS ARGYROS

 

1. PERSONAL

NAME: Ioannis K. Argyros

PLACE OF BIRTH: Athens, Greece.

CITIZENSHIP: USA

ADDRESS: Cameron University, Department of Mathematical Sciences, Lawton, OK 73505, USA

E-MAIL: iargyros@cameron.edu

WEB PAGE: http://www.cameron.edu/~ioannisa

LIST OF MR AND CMP ITEMS:

List of papers authored by Argyros, Ioannis, K.: http://www.ams.org/mrlookup

FAX: (580) 581-2616

TELEPHONE(S): (580) 581-2908 (office) or (580) 581-2481 (office of secretary)

(580) 536-8754 (Home)

2. STUDIES

(1)     1983-1984 Ph.D. in Mathematics, University of Georgia, Athens, Georgia

(2)     1982-1983 M.Sc. in Mathematics, University of Georgia, Athens, Georgia

(3)     1974-1979 B.Sc. in Mathematics, University of Athens, Greece

 

3. ACADEMIC EXPERIENCE

(1)     1994-Present Full Professor, Cameron University, USA

(2)     1993-1994 Tenured Associate Professor, Cameron University, USA

(3)     1990-1993 Associate Professor, Cameron University, USA

(4)     1986-1990 Assistant Professor, New Mexico State University, USA

(5)     1984-1986 Visiting Assistant Professor, University of Iowa, USA

(6)     1982-1984 Teaching-Research Assistant, University of Georgia, USA

(7)     1979-1982 Serving the Greek Army, Greece

 

4. SCIENTIFIC ACTIVITY

(A) Fields of Interest/Research Has Been Conducted in:

(1)     Mathematical Analysis:

(a)     Functional analysis,

(b)     Operator theory. Worked on existence, uniqueness and solvability of Polynomial operator equations on a Banach space,

(c)     Multilinear operator theory,

(d)     Fixed point theory,

(e)     Numerical functional analysis,

(f)      Numerical analysis,

(g)     Applied analysis,

(h)     wavelets.

(2)     Applied Mathematics/Analysis:

(a)     Numerical solution of ordinary-partial differential-integral-functional equations on parallel computers;

(b)     Numerical methods;

(c)     Acceleration of convergence;

(d)     Numerical simulation; numerical approximation; interval arithmetic;

(e)     Numerical algebraic or transcendental equations;

(f)      Mathematical programming; optimization and variational techniques;

(g)     Computer arithmetic and numerical analysis; computer aspects of numerical algorithms;

(h)     Computer networks; discrete mathematics in relation to computer science;

(i)       Theory of data;

(j)      Applications in mechanics, physics, chemistry, biology, technology, and economics.

(3)     Management Science

(4)     Wavelet and Neural Networks

(5)     Mathematical Economics (oligopoly theory, theory of games).

(6)     Mathematical Physics (elasticity, kinetic theory of gasses, astrophysics, mechanics)

The American Mathematical Society subject classification codes for the above interests are: 12, 15, 26, 28, 34, 35, 39, 40, 45, 46, 47, 49, 65, 68, 85, 90.

Most problems in applied sciences can be brought in the form

F(x) = 0,

where F is an operator on some appropriate space. For example the above equation may be a linear or a nonlinear system of equations on the nth dimensional Euclidean space.

I derived such a system when I solved:

(a)     a case of the Chandrasekhar's integral equation (Nobel Prize of Physics, 1983). This equation solves the problem of determination of the angular distribution of the radiant flux emerging from a plane radiation field;

(b)     a problem from nonlinear elasticity theory, which pertains to the buckling of a thin shallow spherical shell clamped at the edge and under uniform external pressure;

(c)     the problem of existence and uniqueness of equilibrium in oligopoly markets. Oligopoly is the state of industry where firms produce homogeneous goods (or close substitutes) and sell their products in a homogeneous market;

(d)     problems coordinating traffic at airports and highways;

(e)     problems involving the construction of safe bridges or buildings;

(f)      problems involving the location of moving objects like: missiles, airplanes, satellites, spaceships;

(g)     models describing the rate with which certain diseases (e.g. cancer) or infections spread on humans or animals;

(h)     models describing population growth or decay (e.g. bacteria on human skin or human population growth or decay). These models help us predict supplies needed for the preservation of human species;

(i)       models describing the behavior of economic markets (e.g. Wall Street Stock Market).

Note that the above is a very incomplete list of physical phenomena that can be brought in the form of the above equation. I just listed the areas where I have contributed with my research manuscripts, books and lectures.

Solutions of the above equation can be approximated by carefully designed numerical algorithms called Newton-like methods with the assistance of computers. Such numerical methods have been described in my published peer-reviewed manuscripts and books and lectures in computational mathematics.

(B) Editing

1.       I am the founder and Editor-in-Chief of the Southwest Journal of Pure and Applied Mathematics.  This is a peer-reviewed purely electronic journal established in 1995 at Cameron University (1995-2004). ISSN 1083-0464. Web Page: http://rattler.cameron.edu/swjpam/swjpam.html

Serving at the editorial board:

2.       Journal of Applied Mathematics and Computing (1997-present). ISSN 1229-9502.

3.       Advances in Nonlinear Variational Inequalities (ANVI) (International Publications USA) (1999-present). ISSN 1092-910X.

4.       Computational Analysis and Applications (Plenum Publ.) (1998-2000). ISSN 1521-1398.

5.       International Journal of Computational and Numerical Analysis and Applications, ISSN 1311-6789 (2000-present), (IJCNAA).

6.       International Journal of Pure and Applied Mathematics, ISSN 1311-8080, (2001-present), (IJPAM).

7.       Mathematical Sciences Research Journal (2002-present), ISSN 1537-5978.

8.       International Review of Pure and Applied Mathematics, (2004-present) Serial Publications

9.       International Journal of Applied Mathematical Sciences (2004-present) Global Publications, ISSN 09730176

10.    Journal of Applied Functional Analysis (2003-2005), Nova Science Corp.

11.    International Journal of Theoretical and Applied Mathematics (2005-Present), Serials Publications.

12.    Communications on Applied Nonlinear Analysis, (2006-Present), International Publications.

13.    Advances in Nonlinear Analysis and Applications (ANAA), (2006-Present),Serial Publications.

14.    Mathematics Applied in Science and Technology, (MAST), (2006-Present), http://www.ripublication.com/mast.htm

15.    Antarctica Journal of Mathematics (2006-Present), http://www.angelfire.com/0k3/prof/journa.html

16.    Polimetrica,Polimetrica Publisher,Corso Milano,Italy (2006-Present),Web Page: http://www.polimetrica.com

17.    Punjab University Journal of Mathematics (2006-Present).

18.    Mathematical Reviews of the American Mathematical Society (August 2006-Present).

19.    Journal of the Korean Society of Mathematics Education Series B. Pure and Applied Mathematics (Associate Editor January 2007-Present). ISSN 1226-0657.

20.    Arabian Journal of Mathematics and mathematical Sciences (AJMMS) (November 2006-Present).

21.    East Asian Journal of Mathematics, (Summer 2007-Present).

22.    Advances and Applications in Mathematical Sciences, July 27, 2008-Present.

23.    International Journal of Mathematics and Computation, 2009-Present.

24.    Communications of the Korean Mathematical Society, Jan 1, 2010-Present.

25.    Applied mathematical and Computational Sciences, 11-9-2009-Present.

26.    Applied Mathematics and Computation (Elsevier,Associate Editor) 1-2010-Present.

27.    J. Mathematical and Computational sciences,ISSN:1927-5307

28.    Contemporary mathematics and statistics

29.    Communicatons in nonlinear analysis

30.    ISRN applied mathematics

31.    ANTA,Analyse numerique and approximation.

 

(C) Book and  Grant Reviewer

1.       Elementary Numerical Analysis by Kendall Atkinson, University of Iowa, published in 1992 by John Wiley & Sons.

2.       Moduli of Continuity and Global Smoothness Preservation in Approximation Theory. Reviewed  for Springer-Verlag Publishers, World Scientific Publishing Company, Elsevier Sciences B.V., Birkhauser, and CRC Press, 1998.

3.       A Handbook on Analytic-Computational Methods and Applications. Reviewed for Plenum Publ. Corp., World Scientific Publishing Company, 1999.

4.       Proklu's Comments on the First Book of Euclid. Vol. 2, ISBN 960-8333-008, 2002, Evangelos Spandagos. I wrote the Introduction in English, AITHRA Publ., Athens, Greece.

5.       College Algebra, 4th Edition, 2003 by Aufmann, Barker, Nation published by Houghton Mifflin.

6.       On behalf of the U.S. Civilian Research and Development Foundation (CRDF) located in Washington D.C. Grant Proposal #12476 entitled: Optimal methods for computing singular integrals, solving singular integrals and applications to geophysics and wave scattering of small bodies of arbitrary shapes (2003)(Russian Federation).

7.       On behalf of Duxbury Press, CA, USA, the draft of the textbook “Statistical Literacy for Citizen(tentative title)”, by Daniel Schaffer. My report was submitted in November,2004.

8.       On behalf of Springer-Verlag(Lecture Series) the textbook entitled:”Iterative Approximation of Fixed Points”by Vasile Berinde.

9.       On behalf of U.S. Civilian Research and Development Foundation(CRDF) Grant Proposal #144038,144002,144009,144015.My id # is 17603.Contact:Jennifer MacNair,Staff Assistant Cooperative Grants Program(Serbian Republic).

10.    On behalf of U.S. Civilian Research and Development Foundation (CRDF) Grant Proposal #15909,Fall 2006.

11.    On behalf of Wiley and Sons Publ.Co.For possible publication: Undergraduate book Entitled:”Trigonometry” by Cynthia Young.,2007.

12.    On behalf of Wiley and Sons, Publ. Co.For possible publication: Undergraduate book, entitled: “Algebra and Trigonometry by Cynthia Young,2007.

13.    On behalf of (CRDF) Grant Proposal #15912,Fall 2007.

14.    On behalf of Prentice Hall Publ. Co. For possible publication,Undergraduate book,entitled: “College Algebra: by Barnett,Ziegler and Byleen,  eighth edition, Spring 2007.

15.    Fondecyt-Proposal 1095025 .On behalf of the Chilean government Author Dr. Sergio Plaza, Contact Maria Elena Boisier ,and Eriac Saavedra Mathematics Project coordinators,email:https://evalcyt.conicyt.cl,and esaavedra@conicyt.cl, October  27, 2008.

16.    On behalf of the Republic of Serbia, Ministry of Science and Technological Development. Grant Proposal Reviewer . Project Number ON174025.Project Name:Problems in Nonlinear Analysis,operator,Theory,Topology and Applications ,Investigator Dr. Vladimir Rakocevic.

 

(D) Scientific Papers Reviewer

I have reviewed a total of 435 papers for:

1.       Journal of Computational and Applied Mathematics

2.       P.U.J.M.

3.       Mathematica Slovaca

4.       Pure Mathematics and Applications (PUMA)

5.       Southwest Journal of Pure and Applied Mathematics

6.       IMA Journal of Numerical Analysis

7.       Journal of Optimization Theory and Its Applications

8.       Computer Physics Communications

9.       SIAM Journal on Numerical Analysis

10.    Computational and Applied Mathematics, CAM 97, 98, 99, Edmond, OK, USA

11.    Applied Mathematics Letters

12.    Illinois Journal of Mathematics

13.    Korean Journal of Computational and Applied Mathematics

14.    Proceeding of the Cambridge Mathematical Society

15.    Applicable Analysis

16.    Journal of Applied Mathematics and Optimization

17.    Computers and Mathematics with Applications

18.    Computational and Applied Mathematics

19.    Computational Analysis and Applications

20.    Tamkang Journal of Mathematics

21.    Soochow Journal of Mathematics

22.    Portugaliae Mathematica

23.    Aequationes Mathematicae

24.    Advances in Nonlinear Variational Inequalities (ANVI)

25.    Journal of Mathematical Analysis and Applications

26.    Journal of Complexity

27.    SIAM Journal of Scientific Computing

28.    International Journal of Mathematics and Mathematical Sciences

29.    AMS Mathematics of Computation

30.    BIT, Numerical Mathematics

31.    Applied Analysis

32.    Journal of Applied Mathematics and Computing

33.    Central European Journal of Mathematics

34.    Applied Numerical Mathematics

35.    Korean Journal of Mathematics in Education

36.    Journal of Integral Equations with Applications

37.    Bulletin of The Malaysian Mathematical Society

38.    Acta Mathematica Sinica

39.    Electronic Journal of Differential Equations

40.    Studia Mathematica Hungarica

41.    Mathematical Reviews of the American Mathematical Society

42.    Mathematics of Computation of the American Mathematical Society

43.    PUJM

44.    International Journal of Computer Mathematics

45.    Zhejiang University Journal of Mathematics

46.    Physics Letters A.

47.    Numerical Algorithms

48.    Journal of Inequalities and Applications

49.    Proceedings of the American Mathematical Society

50.    Journal of Applied Mathematics and Stochastic Analysis

51.    Fixed Point Theory and Applications

52.    Applicationes Mathematicae

53.    European Journal of Operations Research.

54.    Nonlinear Analysis.

55.    Fuzzy sets and systems

56.    American Mathematical Monthly

57.    Mathematical Inequalities  and Applications

58.    Journal of Mathematical Sciences:Advances and Applications

59.    SINUM

60.    Archivum Mathematicarum

61.    Appled Mathematics and Computation

62.    Numerical Functional Analysis and Optimization

63.    Applied Mathematics A..J.Chinese University

64.    Fixed Point Theory and Applications

65.    MPE (Hindawi)

66.    Journal of Inequalities and Applications

67.    Albanian Journal of Mathematics

68.    Optimization

69.    Europen Journal of Operations Research

70.    Mathematica Slovaca

71.    Cubo

72.    Computational Methods in Applied Mathematics

73.    Hacettepe Journal of mathematics and Stataistics

74.    Applied Numerical Mathematics

75.    Kuwait Journal of Science and Engineering

 

(E) Grants Received

1.       New Mexico State University Grant, (1986), #1-3-43841, RC #87-01

2.       New Mexico State University Grant, (1987), #1-3-4-44770.

3.       U.S.A. Army (1988-1990), #DAEA, 26-87-R-0013 (F.M.) Army (jointly with the Mechanical Engineering Department at New Mexico State University). Topic: "Solution of differential equations on parallel computers"

4.       Cameron University, Research support, July 1992, June 1998

5.       Cameron University, Academic Initiatives Award (#6110), 2004-2005.

6.       NSF 2007 EPSCOR INFRASTRUCTURE IMPROVEMENT PROPOSAL Participant (Leading Investigator Dr. Henry Neeman). 

 

(F) Supervising Graduate Students

1.       The following Ph.D. students have obtained their Ph.D. degree under my supervision:

2.       Losta Mansor, Ph.D. dissertation title: Numerical Methods for Solving Perturbation Problems Appearing in Elasticity and Astrophysics, 1989

3.       Joan Peeples, Ph.D. dissertation title: Point to Set Mappings and Oligopoly Theory, 1989 Member, Doctoral Examination Committee:

4.       Aomar Ibenbrahim, Spring 1987

5.       Maragoudakis Christos, Spring 1988 (Dean's Representative for both, Electrical Engineering Department)

6.       Bellal Hossain, Fall 1996, University of Calcutta, India

7.       Sri Pulak Guhathakurta, Spring 1998, University of Calcutta, India

8.       Tariq Iqtadar Khan, Spring 2003, Aligarh University, India

9.       Landlay  Khan,Fall 2005, Aligarg University,India,Thesis title:Common Fixed Point Theorems for some families of nonself mappings in metrically convex spaces.

10.    Nadeem Ahmad, Summer 2007, Ph. D. Thesis external supervisor,Thesis title:Geometric Modelling using subdivision techniques, PUJM, Lahore Pakistan.

11.    Syed Abbas ,Fall 2009,Ph.D. Thesis Title: Almost periodic solutions of nonlinear functional differential equations,Indian Institute of Technology Kanpur, India.

12.    Kashif Rehan, Spring 2010,Phd. Thesis:Subdivision Schemes:The new paradigm in computer aided geometric design. University of Punjab ,Lahore Pakistan.

Chair, Master's Examination Committee

1.       Mitra Ashan, Spring 1987

2.       Christopher Stuart, Spring 1988

3.       Anis Shahrour, Fall 1988

Member, Master's Examination Committee

1.       Juji Hiratsuka, Spring 1987 (Dean's Representative, Art Department)

2.       Alice Lynn Bertini, Spring 1988

3.       Daniel Patrick Eshner, Summer 1989 (Dean's Representative, Computer Science)

(G) Committee Member for Hiring-Promotion-Tenure

I have served as a committee member for:

(a)     Hiring: Cameron University (USA), every year, Punjab University (Pakistan), 2000 and 2002

(b)     Promotion-Tenure: Cameron University (USA), Sultan Qaboos University, Sultanate of Oman, Sam Houston State University (USA), Punjab University (Pakistan), 2001

(c)     Promotion Dr. Marwan S. Abualrub,University of Jordan,2011.

(H) M. Sc. and Ph. D.  Dissertations

1.       A Contribution to the Theory of Nonlinear Operator Equations in Banach Space, Master of Science Dissertation, University of Georgia, GA, U.S.A., 1983.

2.       Quadratic Equations in Banach Spaces, Perturbation Techniques and Applications to Chandrasekhar's and Related Equations, Doctor of Philosophy Dissertation, University of Georgia, GA, U.S.A., 1984.

 

(I) Books and Monographs Published

1.       The Theory and Applications of Iteration Methods, CRC Press, Inc., Systems Engineering Series, Boca Raton, Florida, 1993, Math. Rev. 65b:65001, Zbl. Math. 65J, 65052, (W.C. Rheinboldt (Pittsburgh)), (1992), 844-441, ISBN 0-8493-8014-6. (Textbook)

2.       A Unified Approach for Solving Nonlinear Operator Equations and Applications, West University of Timisoara, Department of Mathematics, Mathematical Monographs, 62, Publishing House of the University of Timisoara, Timisoara, 1997, AMS Math. Reviews 99i65060. (Monograph)

3.       The Theory and Application of Abstract Polynomial Equations, St. Lucie/CRC/Lewis Publishers, Mathematics Series, Boca Raton, Florida, USA, 1998, ISBN 0-8493-8702-7. Springer-Verlag Publ., New York is publishing this text since 2000 by taking over from CRC. (Textbook), MR 1818212

4.       Dictionary of Comprehensive Dictionary of Mathematics: Analysis, Calculus and Differential Equations, (Contributing Author), Editor: Douglas, N. Clark, Chapman-Hall/CRC/Lewis Publishers, Boca Raton, Florida, USA, 1999, ISBN 0-8493-0320-6. (Textbook)

5.       Computational Methods for Abstract Polynomial Equations, West University of Timisoara, Department of Mathematics, Mathematical Monographs, 68, Publishing House of the University of Timisoara, Timisoara, 1999. (Monograph), MR 1997218

6.       A Survey of Efficient Numerical Methods for Solving Equations and Applications, Kyung Moon Publishers, Seoul, Korea, 2000, ISBN 8972824828. (Textbook)

7.       A Unified Approach for Solving Equations, Part I: On Infinite-Dimensional Spaces, Handbook of Analytic Computational Methods in Applied Mathematics, Chapman and Hall/CRC Press, Inc., Boca Raton, Florida, 2000, Chapter 5, pp. 201-254, ISBN 1-58488-135-6. (Monograph)

8.       A Unified Approach for Solving Equations, Part II: On Finite-Dimensional Spaces, Handbook on Analytic Computational Methods in Applied Mathematics, Chapman and Hall/CRC Press, Inc., Boca Raton, Florida, 2000, Chapter 6, pp. 255-308, ISBN 1-58488-135-6. (Monograph)

9.       Two Contemporary Computational Aspects of Numerical Analysis, Applied Math. Reviews, Volume 1, World Scientific Publishing Corp., River Edge, NJ, 2000, ISBN 981-02-4339-1. (Monograph)

10.    Advances in the Efficiency of Computational Methods and Applications, World Scientific Publ. Co., River Edge, NJ, 2000, ISBN 981-02-4336-7. (Textbook)

11.    Iterative Methods for Solving Equations Appearing in Engineering and Economics. Kyung Moon Publ., Seoul, Korea, 2001, ISBN 89-7282-512-3. (Textbook)

12.    Contemporary Computational Methods in Numerical Analysis, Part I. Methods Involving Fréchet-Differentiable Operators of Order One, Mathematical Monographs (Timisoara), 74, West University of Timisoara, Department of Mathematics, Publishing House of the University of Timisoara, Timisoara, Romania,2002 viii+170 pp, MR 2053593(2005a:65051a), (Monograph).

13.    Contemporary Computational Methods in Numerical Analysis, Part II: Methods Involving Fréchet-Differentiable Operators of Order m (m > 2),  Mathematical Monographs (Timişoara), 75, West University of Timisoara, Department of Mathematics, Publishing House of the University of Timisoara, Timisoara, Romania,2002 pp. i-viii,171-326 pp.MR 2053594(2005a:65051b) (Monograph).

14.    Newton Methods, Nova Science Publ.Corp., Hauppauge, New York, USA, 2005, ISBN:1-59454-052-7,(Textbook).

15.    Approximate Solution of Operator Equations with Applications, World Scientific Publ. Co.,Pte.Ltd.,Hackensack,NJ,2005,USA,ISBN:981-256-365-2, 512 pages (Textbook).

16.    Computational Theory of Iterative Methods, Series: Studies in Computational Mathematics 15, Editors, ;C. K. Chui, and L. Wuytack, Elsevier Publ. Co., New York, USA, 2007, (Textbook), ISBN 978-0-444-53162-9.

17.    Convergence and applications of Newton-type iterations, Springer –Verlag  Publ., 2008, ISBN-13:978-0-387-72741-7e and ISBN-13:978-0-387-72743-1.

18.    Efficient methods for solving equations and variational inequalities, Polimetrica Publ. Comp., 2009, 603 pages, ISBN: 978-88-7699-149-3

19.    Aspects of computational theory for certain iterative methods, Polimetrica Publ. Comp., 2009, 571 pages, ISBN: 978-88-7699-151-6.

20.    Mathematical  Modelling with Applications in Biosciences, and Engineering, Nova Science Publ. Corp., Hauppauge, New York ,USA,2011,ISBN 978-61728-944-6

21.    Advances on iterative procedures,Nova Science  Publ.Corp.Hauppauge ,New York,USA2011,ISBN 978-1-61209-522-6.

22.    Numerical methods for equations and its applications,CRCPress/Taylor and Francis Group, New York 2012,ISBN:978-1-57808-753-2.

Books and Monographs Under Preparation/Accepted

23.    .  

(J1) UNDERGRADUATE RESEARCH

(1) Geneva Howard, Masters student in Education , Math 4492, (Independent study), Spring 2003.

Paper Title: Linear Programming in Mathematics Education.

Poster Presentation, Oklahoma Research Day, 2003, Edmond Oklahoma

(2) Martina Melrose, Math  4493  (independent study), Spring 2004.

Paper title: Linear and Nonlinear Programming survey.

Poster Presentation, Oklahoma Research Day 2004, Edmond Oklahoma.

(3) Ivica Ristovski, Spring 2005.

Paper Title: On an inequality from Applied Analysis

Paper Presentation at the Torus conference,  February 25,2005.

(4)     Gabriel Vidal

Paper title: Observations on Newton’s method.

Poster Presentation,Oklahoma  Research Day 2005, Edmond Oklahoma, November 11.

(5) Irene Corriette, and Ms Sabina Sadou

Paper Title: Advances on Newton’s method.

Poster Presentation, Okalhoma Research Day 2006, November 20, Edmond Oklahoma.

(6) Jingshu  Zhao,

Paper Title: Applications of sequences and series to numerical methods.

Paper Presentation, Oklahoma Research Day 2009, Oklahoma

(7)Jingshu Zhao

Paper Presentation, Torus Conference, Wichita Falls,  February  27,  2010.

(8)Shobhakhar  Adhikari

Poster Presentation, Oklahoma Research Day 2010 CU, Lawton ,OK November 12 ,2010.

Poster Presentation, Oklahoma Research Day 2011,CU Lawton,OK October ,2011.

(J2) RESEARCH ARTICLES

The scientific papers listed below have been published in the following countries and at the top refereed journals in the following countries repeatedly:

America: U.S.A., Brazil, Canada, Chile

Europe: U.K., Sweden, Belgium, Holland, Spain, Germany, Austria, Hungary, Slovakia, Romania, Poland, Yugoslavia, Italy, Chech Republic,Bulgaria

Asia: People's Republic of China, Republic of China, India, Pakistan, Japan, Saudi Arabia, Korea, Singapore, Malaysia

Australia: Australia

A 9% of the scientific papers listed below have been published jointly with Professors Mohammad Tabatabai  (Cameron, USA), Dong Chen (University of Arkansas, USA), Ferenc Szidarovszky (University of Arizona, USA), Losta Mansor (Libya), Emil Catinas and Ion Pavaloiu (Romania), Ram Verma (Florida, USA), Jose Gutierrez (Spain),M. Hernandez (Spain), J. Ezquerro, (Spain), Huang Zhengda  (USA, China), Dr. Uko (USA), Dr. Hilout (France, Morocco), .Dr. R. Ren, Dr. S. Chen (P.R. China)

1.             Quadratic equations and applications to Chandrasekhar's and related equations, Bull. Austral. Math. Soc., Vol. 32, 2 (1985), 275-292; Not. Amer. Math. Soc., 85T-46-142; Z.F.M.6074063 (1987); Math. Rev. 87d: Gerard Lebourg  (Paris).

2.             On a contraction theorem and applications, Proc. Amer. Math. Soc., Symposium on Nonlinear Functional Analysis and Applications, Berkeley, CA, U.S.A., 1983, 45, 1 (1986), 51-53; Math. Rev. 87h: 65108, Sh. Singh, Z.F.M.6224077 (1988).

3.             Iterations converging to distinct solutions of some nonlinear equations in Banach space, Internat. J. Math. & Math. Sci., Vol. 9, No. 3 (1986), 585--587; Z.F.M.61447044 (1986); Math. Rev. 87j47097, P.P. Zabrejko (Minsk).

4.             On the cardinality of solutions of multilinear differential equations and applications, Internat. J. Math. & Math. Sci., Vol. 9, No. 4 (1986), 757-766; Math. Rev. 88e34017, Achmadjon Soleev (Samarkand); Z.F.M.66334008 (89), A. Soleev.

5.             Uniqueness-Existence of solutions of polynomial equations in linear space, P.U.J.M., Vol. XIX (1986), 39-57; Z.F.M.62547050 (1988); Math. Rev.88g47116, B.G. Pachpatte (6-Mara).

6.             On a theorem for finding "large" solutions of multilinear equations in Banach space, P.U.J.M., Vol. XIX (1986), 29-37; Z.F.M.62547051 (1988); Math.Rev. 88g47115, B.G. Pachpatte (6-Mara).

7.             On the approximation of some nonlinear equations, Aequationes Mathematicae, 32 (1987), 87-95; Z.F.M.61447043 (1986); Math. Rev. 88g47124, P.P. Zabrejko (Minsk).

8.             An improved condition for solving multilinear equations, P.U.J.M., Vol. XX (1987), 43-46; Math. Rev. 89c47065; Z.F.M.64747015, (1989).

9.             On a class of nonlinear equations, Tamkang J. Math., Vol. 18, No. 2 (1987); 19-25; Math. Rev. 89f47091, Ramendra Krishna Bose (1-SUNYF); Z.F.M.65347042, (1989), J. Appel.

10.          On polynomial equations in Banach space, perturbations, techniques and applications, Internat. J. Math.& Math. Sci., Vol. 10, No. 1 (1987), 69-78; Math. Rev. 88c47123, Heinrich Steinlein (Munich); Z.F.M.61747038, (1987).

11.          A note on quadratic equations in Banach space, P.U.J.M., Vol. XX (1987), 47-50; Math. Rev. 89c47076; Z.F.M.64747016, (1989).

12.          Quadratic finite rank operator equations in Banach space, Tamkang J. Math., Vol. 18, No. 4 (1987); 8-19; Z.F.M.66247011 (89); Math. Rev. 89k47100, Nicole Brillouet-Belluot (Nantes).

13.          On some theorems of Mishra Ciric and Iseki, Mat. Vesnik, Vol. 39 (1987), 377-380; Math. Rev. 89c54083; Z.F.M.64854035, (1989).

14.          An iterative solution of the polynomial equation in Banach space, Bull. Inst. Math. Acad. Sin., Vol. 15, No. 4 (1987), 403-410; (Math. Rev. Author index 1989), 47H17, 46G99, 58C15.

15.          A survey on the ideals of the space of bounded linear operators on a separable Hilbert space, Rev. Acad. Ci. Exactas Fis. Quim. Nat. Zaragoza, II. Ser. 42 (1987), 24-43; Math. Rev. 89g47059.

16.          On the solution by series of some nonlinear equations, Rev. Acad. Ci. Exactas Fis. Quim.Nat. Zaragoza, II. Ser. 42 (1987), 18-23; Z.F.M.64947048, (1989); Math. Rev. 90f65085, V.V. Vasin (Sverdlosk).

17.          Newton-like methods under mild differentiability conditions with error analysis, Bull. Austral. Math. Soc., Vol. 37, 1 (1988), 131-147; Z.F.M.62965061, (1988), S. Reich; Math. Rev. 89b65142, A.V. Dzhishkariani (Tbilisi).

18.          On Newton's method and nondiscrete mathematical induction, Bull. Austral. Math. Soc., Vol. 38 (1988), 131-140; Math. Rev. 90a65136, A.M. Galperin (Ben-Gurion Intern. Airp.).

19.          On a class of nonlinear integral equations arising in neutron transport, Aequationes Mathematicae, Vol. 35 (1988), 99-111; Math. Rev. 89M47058, H.E. Gollwitzer (1-DREX).

20.          New ways for finding solutions of polynomial equations in Banach space, Tamkang J. Math., Vol. 19, 1 (1988), 37-42; Math. Rev. 90f47093, V.V. Vasin (Sverdlosk).

21.          On a new iteration for solving polynomial equations in Banach space, Funct. et Approx. Comment. Math., Vol. XIX (1988); Math. Rev. 91d:65082, Xiaojun Chen.

22.          Conditions for faster convergence of contraction sequences to the fixed points of some equations in Banach space, Tamkang J. Math., Vol. 19, 3 (1988), 19-22; Math. Rev. 90j47074, Roman Manka (Mogilno).

23.          Approximating the fixed points of some nonlinear equations, Mathem. Slovaca, 38, No. 4 (1988), 409-417; Z.F.M.667 (1989), S.L. Singh. Math. Rev. 90g47109 (O.P. Kapoor (6-11TK)).

24.          Some sufficient conditions for finding a second solution of the quadratic equation in Banach space, Mathem. Slovaca, 4 (1988); Math. Rev. 90g47108 (O.P. Kapoor (6-11TK)).

25.          Concerning the approximation solutions of operator equations in Hilbert space under mild differentiability conditions, Tamkang J. Math., Vol. 19, No. 4 (1988), 81-87; Math. Rev. 91g:65137, P.S. Milojevic.

26.          The Secant method and fixed points of nonlinear equations, Monatshefte fur Mathematik, 106 (1988), 85-94; Z.F.M.65265043 (1989); Math. Rev. 90b6511, A.M. Galperin, Ben-Gurion Intern. Airport.

27.          An iterative procedure for finding "large" solutions of the quadratic equation in Banach space, P.U.J.M., Vol. XXI (1988), 13-21; Math. Rev. 91g:65136, P.S. Milojevic.

28.          Vietta-Like relations in Banach space, Rev. Acad. Ci. Exactas Fis. Quim. Nat. Zaragoza, I, Ser. 43 (1988), 103-107; Math. Rev. 47f47095, V.V. Vasin (Sverdlovsk).

29.          A global theorem for the solutions of polynomial equations, Rev. Acad. Ci. Exactas Fis. Quim. Nat Zaragoza, I, Ser. 43 (1988), 93-101; Math. Rev. 90f47094, V.V. Vasin, (Sverdlosk).

30.          Concerning the convergence of Newton's method, P.U.J.M., Vol. XXI (1988), 1-11; Math. Rev. 91g:65135, P.S. Milojevic.

31.          On the number of solutions of some integral equations arising in radiative transfer, Internat. J. Math.& Math. Sci., Vol. 12, No. 2 (1989), 297-304; Math. Rev. 90h86004, S. Rajasekar (Ticuchirapalli).

32.          On the approximate solutions of operator equations in Hilbert space under mild differentiability conditions, J. Pure & Appl. Sci., Vol. 8, No. 1 (1989), 51-56.

33.          On the fixed points of some compact operator equations, Tamkang J. Math., Vol. 20,  No. 3 (1989), 203-209; Math. Rev. 91a47088, Jing Xian Sum (PRC-Shan).

34.          Error bounds for a certain class of Newton-like methods, Tamkang J. Math., Vol. 20, No. 4  (1989); Math. Rev. 91k:65096, J.W. Schmidt.

35.          Concerning the convergence of iterates to fixed points of nonlinear equations in Banach space, Bull. Malays. Math. Soc., Vol. 12, 2 (1989), 15-24; Math. Rev. Author index 1991.

36.          A series solution of the quadratic equation in Banach space, Chinese J. Math., Vol. 27, No. 4 (1989); Math. Rev. 90k47131.

37.          On a fixed point in a 2-Banach space, Rev. Acad. Ciencias, Zaragoza, 44 (1989), 19-21; Math. Rev. 91a47077; Math. Rev. 91a:47077.

38.          Some matrices in oligopoly theory, New Mexico J. Sci., 29, 1 (1989), 22.

39.          On a theorem of Fisher and Khan, Rev. Acad. Ciencias, Zaragoza, 44 (1989), 13-17; Math. Rev. 91d:54048, Sehie Park.

40.          On quadratic equations, Mathematica-Rev. Anal. Numer. Theor. Approximation, 18, 1 (1989), 19-26; Math. Rev. 91f:47094.

41.          Concerning the approximate solutions of nonlinear functional equations under mild differentiability conditions, Bull. Malays. Math. Soc., Vol. 12, 1 (1989), 55-65; Math. Rev. 91k:47164, V.V. Vasin.

42.          On the convergence of certain iterations to the fixed points of nonlinear equations, Annales sectio computatorica, Ann. Univ. Sci. Budapest. Sect. Computing, 9 (1989), 21-31; Math. Rev. 91k:65095, J.W. Schmidt.

43.          On the secant method and nondiscrete mathematical induction, Mathematica-Revue d'Analyse Numerique et de Theorie de l'Approximation, tome 18, No. 1 (1989), 27-36; Math. Rev. 91j:65104.

44.          On Newton's method for solving nonlinear equations and multilinear projections, Functiones et approximatio Comment. Math., XIX (1990), 41-52; Math. Rev. 92b:4707, Joe Thrash.

45.          Nonlinear operator equations and pointwise convergence, Functiones et approximatio Comment. Math., XIX (1990), 29-39; Math. Rev. 92b:47106, Joe Thrash.

46.          Iterations converging faster than Newton's method to the solutions of nonlinear equations in Banach space, Functiones et approximatio Comment. Math., XIX (1990), 23-28; Math. Rev. 91m:65164.

47.          On some quadratic integral equations, Functiones et Approximmatio, XIX (1990), 159-166; Math. Rev. 92d:47081, Aeinrich Steinlein.

48.          A mesh independence principle for nonlinear equations using Newton's method and nonlinear projections, Rev. Acad. Ciencias. Zaragoza, 45 (1990), 19-35; Math. Rev. 92e:65076a, Mihai Turinci.

49.          Error bounds for the modified secant method, BIT, 30 (1990), 92-100; Math. Rev. 91d:65083, Xiaojun Chen.

50.          Improved error bounds for a certain class of Newton-like methods, J. Approximation Theory and its Applications, (6:1) (1990), 80-98; Math. Rev. 92a:65188, A.M. Galperin.

51.          On the solution of some equations satisfying certain differential equations, P.U.J.M., Vol. XXIII (1990), 47-59; Math. Rev. 92d:65102.

52.          On some projection methods for approximating the fixed points of nonlinear equations in Banach space, Tamkang J. Math., Vol. 21, 4 (1990), 351--357; Math. Rev. 92a:47072, Joe Thrash.

53.          On some projection methods for the approximation of implicit functions, Appl. Math. Lett., Vol. 3, No. 2 (1990), 5-7; Math. Rev. 91b65066.

54.          On the monotone convergence of some iterative procedures in partially ordered Banach spaces, Tamkang J. Math., Vol. 21, No. 3 (1990), 269-277; Math. Rev. 91h:47067, Joe Thrash.

55.          The Newton-Kantorovich method under mild differentiability conditions and the Ptak error estimates, Monatschefte fur Mathematik, Vol. 109, No. 3 (1990); Math. Rev. 91k:65034, J.W. Schmidt.

56.          The secant method in generalized Banach spaces, Appl. Math. & Comput., 39 (1990), 111-121; Math. Rev. 91h:65099.

57.          On the solution of equations with nondifferentiable operators and Ptak error estimates, BIT, 30 (1990), 752-754; Math. Rev. 91k:65099.

58.          On some projection methods for enclosing the root of a nonlinear operator equation, P.U.J.M., Vol. XXIII (1990), 35-46; Math. Rev. 91h:47067, Joe Thrash.

59.          A mesh independence principle for operator equations and their discretizations under mild differentiability conditions, Computing, 45 (1990), 265-268; Math. Rev. 91i:65106.

60.          On Newton's method under mild differentiability conditions, Arabian J. Math., Vol. 15, 1 (1990), 233-239; Math. Rev. 91k:65097, J.W. Schmidt.

61.          Remarks on quadratic equations in Banach space, Intern. J. Math. & Math. Sci., Vol. 13, No. 3 (1990), 611-616; Math. Rev. 91e:47062.

62.          On the improvement of the speed of convergence of some iterations converging to solutions of quadratic equations, Acta Math. Hungarica, Vol. 57/3-4 (1990), 245-252; Math. Rev. 93d:47121, Teodor Potra.

63.          A note on Newton's method, Rev. Acad. Ciencias Zaragoza, 45 (1990), 37-45; Math. Rev. 92e:65076b, Mihai Turinici.

64.          On the solution of compact linear and quadratic operator equations in Hilbert space, Rev. Acad. Ciencias Zaragoza, 45 (1990), 47-52; Math. Rev. 92e:65076c, Mihai Turinici.

65.          On some generalized projection methods for solving nonlinear operator equations with a nondifferentiable term, Bull. Malays. Math. J., Vol. 13, No. 2 (1990), 85-91; Math. Rev. 92g:65065, Gerard, Lebourg.

66.          Comparison theorems for algorithmic models, Applied Math. and Comput., Vol. 40, No. 2  (Nov. 1990), 179-187; Math. Rev. 92b:65102.

67.          On an iterative algorithm for solving nonlinear equations, Beitrage zur Numerischen Math. (Renamed Z.A.A.), Vol. 10, No. 1 (1991), 83-92; Math. Rev. 93b:47132.

68.          On time dependent multistep dynamic processes with set valued iteration functions on partially ordered topological spaces, Bull. Austral. Math. Soc., Vol. 43 (1991), 51-61; Math. Rev. 92d:65107, Tetsuro Yamamoto.

69.          Error bounds for the secant method, Math. Slovaca, Vol. 41, 1 (1991), 69-82; Math. Rev. 92j:65086, K. Bohmer.

70.          On the approximate solutions of nonlinear functional equations under mild differentiability conditions, Acta Math. Hungarica, Vol. 58 (1-2) (1991), 3-7; Math. Rev. Author index, 1992.

71.          On the convergence of some projection methods with perturbation, J. Comput. and Appl. Math., 36 (1991), 255-258; Math. Rev. 92f:65065, H.R. Shen.

72.          On an application of a modification of the Zincenko method to the approximation of implicit functions, Z.A.A., 10 3 (1991), 391-396; Math. Rev. 93b:47133, Tetsuro Yamamoto.

73.          On some projection methods for solving nonlinear operator equations with a nondifferentiable term, Rev. Academia de Ciencias, Zaragoza, 46 (1991), 17-24; Math. Rev. 92m:47133.

74.          Integral equations for two-point boundary value problems, Rev. Academia de Ciencias, Zaragoza, 46 (1991), 25-35; Math. Rev. 93b:65205, Jan Pekar.

75.          A fixed point theorem for orbitally continuous functions, Pr. Rev. Mat., Vol. 10, No. 7 (1991), 53-57; Math. Rev. 93d:47101, Ramendra Krishna Bose.

76.          Bounds for the zeros of polynomials, Rev. Academia de Ciencias, Zaragoza, 47 (1992), 61-66; Math. Rev. 94a:26035, N.K. Govil.

77.          On a class of quadratic equations with perturbation, Functiones et Approximmatio, XX (1992), 51-63; Math. Rev. 94a:45011, P.M. Gupta.

78.          On a new iteration for finding "almost" all solutions of the quadratic equation in Banach space, Studia Scientiarum Mathematicarum Hungarica, 27, (3-4) (1992), 361-368; Math. Rev. 94d:65037, J.W. Schmidt.

79.          A Newton-like method for solving nonlinear equations in Banach space, Studia Scientiarum Mathematicarum Hungarica, 27 (3-4) (1992), 369-378; Math. Rev. 94d:65038, J.W. Schmidt.

80.          On the convergence of nonstationary Newton methods, Func. et Approx., Vol. XXI (1992), 7-16; Math. Rev. 95g:65080, A.M. Galperin.

81.          On an application of the Zincenko method to the approximation of implicit functions, Publicationes Mathematicae Debrecen, Vol. 40/1-2 (1992), 43-49; Math. Rev. 93c:47076, A.M. Galperin.

82.          Improved error bounds for the modified secant method, Intern. J. Computer Math., Vol. 43, No. 1+2 (1992), 99-109.

83.          On the midpoint method for solving nonlinear operator equations in Banach spaces, Appl. Math. Letters, Vol. 5, No. 4 (1992), 7-9; Math. Rev. 96b:65061.

84.          On an application of a Newton-like method to the approximation of implicit functions, Math. Slovaca, 42, No. 3 (1992), 339-347; Math. Rev. 93h:65081, J.W. Schmidt.

85.          On the monotone convergence of general Newton-like methods, Bull. Austral. Math. Soc., 45 (1992), 489-502; Math. Rev. 93c:65077.

86.          Convergence of general iteration schemes, J. Math. Anal. and Applic., 168, No. 1 (1992), 42-52; Math. Rev. 93d:65055, S. Sridhar.

87.          Some generalized projection methods for solving operator equations, Jour. Comp. Appl. Math., 39, No. 1 (1992), 1-6; Math. Rev. 92m:65079.

88.          Sharp error bounds for a class of Newton-like methods under weak smoothness assumptions, Bull. Austral. Math. Soc., 45 (1992), 415-422; Math. Rev. 93c:65076.

89.          Approximating Newton-like procedures, Appl. Math. Lett., Vol. 5, No. 1 (1992), 27-29. CMP 1 144362.

90.          On a mesh independence principle for operator equations and the secant method, Acta Math. Hungarica, 60, 1-2 (1992), 7-19; Math. Rev. 94g:65057, A.M. Galperin.

91.          On the solution of quadratic integral equations, P.U.J.M., Vol. XXV (1992), 131-143; Math. Rev. 95j:65177, P. Uba.

92.          On the convergence of generalized Newton-methods and implicit functions, Journ. Comp. Appl. Math., 43 (1992), 335-342; Math. Rev. 93m:65076, J.W. Schmidt.

93.          On a Stirling-like method, P.U.J.M., Vol. XXV (1992), 83-94; Math. Rev. 95j:65062, Anton Suhadolc.

94.          On the approximate construction of implicit functions and Ptak error estimates, P.U.J.M., Vol. XXV (1992), 95-98; Math. Rev. Author Index 1995.

95.          On the numerical solution of linear perturbed two-point boundary value problems with left, right and interior boundary layers, Arabian J. Science and Engineering, 17: 4B (October 1992), 611-624; Math. Rev. 94c:65097.

96.          On the convergence of Newton-like methods, Tamkang J. Math., Vol. 23, No. 3 (1992), 165-170; Math. Rev. 93m:65077, J.W. Schmidt.

97.          On the monotone convergence of algorithmic models, Applied Math. and Comput., 48, (2-3) (1992), 167-176; Math. Rev. 92m:47134, Vincentiu Dumitru.

98.          Approximating Newton-like iterations in Banach space, P.U.J.M., Vol. XXV (1992), 49-59; Math. Rev. 95j:65061, Anton Suhadolc.

99.          On the approximation of quadratic equations in Banach space using finite rank operators, Rev. Academia de ciencias Zaragoza, 47 (1992), 67-76; Math. Rev. 94f:47085.

100.      Remarks on the convergence of Newton's method under Holder continuity conditions, Tamkang J. Math., Vol. 23, No. 4 (1992), 269-277; Math. Rev. 94b:65080, J.W. Schmidt.

101.      On the solution of nonlinear operator equations in Banach space and their discretizations, Pure Mathematics and Applications, Ser. B, Vol. 3, No. 2-3-4 (1992), 157-173; Math. Rev. 94i:65069, C. Ilioi.

102.      On the convergence of optimization algorithms modeled by point-to-set mappings, Pure Mathematics and Applications, Ser. B, Vol. 3, No. 2-3-4 (1992), 77-86; Math. Rev. 94i:90117, Han Ch'ing Lai.

103.      On the convergence of inexact Newton-like methods, Public. Math. Debrecen, Vol. 43, 1-2 (1993), 79-85; Math. Rev. 94h:65064, Carl T. Kelley.

104.      On some projection methods for the solution of nonlinear operator equations with nondifferentiable operators, Tamkang J. Math., Vol. 24, No. 1 (1993), 1-8; Math. Rev. 94m:65097, A.V. Dzhishkariani.

105.      An initial value method for solving singular perturbed two-point boundary value problems, Arabian Journ. Scienc. and Engineer., Vol. 18, 1 (1993), 3-5.

106.      On the solution of nonlinear equations with a nondifferentiable term, Revue D'Analyse Numerique et de Theorie de l'Approximation, Tome 22, 2 (1993), 125-135; Math. Rev. 96a:65092, A.M. Galperin (IL-BGUN; Be'er Sheva).

107.      Some methods for finding error bounds for Newton-like methods under mild differentiability conditions, Acta Math. Hungarica, 61, (3-4) (1993), 183-194; Math. Rev. 94m:65096, A.V. Dzhishkariani.

108.      On the secant method, Publicationes Mathematicae Debrecen, Vol. 43, 3-4 (1993), 223-238; Math. Rev. 95j:47077, R. Kodnar.

109.      Improved error bounds for Newton's method under generalized Zabrejko-Nguen-type assumptions, Appl. Math. Letters, Vol. 6, No. 3 (1993), 75-77; Math. Rev. Author index 1996.

110.      A fourth order iterative method in Banach spaces, Appl. Math. Letters, Vol. 6, No. 4 (1993), 97-98; Math. Rev. Author index 1996.

111.      Newton-like methods and nondiscrete mathematical induction, Studia Scientiarum Mathematicarum Hungarica, 28 (1993), 417-426; Math. Rev. 95b:47084, A.M. Galperin.

112.      Robust estimation and testing for general nonlinear regression models, Appl. Math. and Comp., 58 (1993), 85-101; Math. Rev. 94i:62097, Adrej Pazman.

113.      A mesh independence principle for nonlinear operator equations in Banach space and their discretizations, Studia Scientiarum Math. Hung., 28 (1993), 401-415; Math. Rev. 95b:65077, A.M. Galperin.

114.      Sharp error bounds for the secant method under weak assumptions, P.U.J.M., Vol. XXVI (1993), 54-62; Math. Rev. Author index 1995.

115.      An error analysis of Stirling's method in Banach spaces, Tamkang J. Math., Vol. 24, No. 2 (1993), 115-133; Math. Rev. 94h:65058, A.M. Galperin.

116.      New sufficient conditions for the approximation of distinct solutions of the quadratic equation in Banach space, Tamkang J. Math., Vol. 24, No. 4 (1993), 355-372; Math. Rev. 95f:47090.

117.      On the convergence of inexact Newton methods, Chinese J. Math., Sept. Vol. 21, No. 3 (1993), 227-234; Math. Rev. 94f:47088, Mihai Turinici.

118.      On the solution of equations with nondifferentiable operators, Tamkang J. Math., Vol. 24, No. 3 (1993), 237-249; Math. Rev. 94i:65070, C. Ilioi.

119.      Sufficient conditions for the convergence of general iteration schemes, Chinese J. Math., Vol. 21, No. 2 (1993), 195-205; Math. Rev. 94f:47087, Mihai Turinici.

120.      On a two-point Newton method in Banach spaces of order four and applications, (1993), Proceedings of the 9th Annual Conference on Applied Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), Rev. Academia de Ciencias, Zaragoza, 50 (1995), 5-13; Math. Rev. Author index 1996.

121.      On a two-point Newton method in Banach spaces of order three and applications, Proceedings of the 9th Annual Conference on Applied Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), 24-37; P.U.J.M., Vol. 27 (1994), 10-22; Math. Rev. Author index 1996.

122.      On a two point Newton-method in Banach spaces and the Ptak error estimates, Proceedings of the 9th Annual Conference on Applied Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), 8-24; Communications on Applied Nonlinear Analysis, 7, (2000), 2, 87-100.

123.      Sufficient convergence conditions for iteration schemes modeled by point-to-set mappings, Proceedings of the 9th Annual Conference on Applied Mathematics, CAM 93, University of Central Oklahoma, Edmond, (1993), 48-52.  Applied Mathematics Letters, Vol. 9, No. 2 (1996), 71-73; Math. Rev. Author index 1996.

124.      On the convergence of a Chebysheff-Halley-type method under Newton-Kantorovich hypotheses, Appl. Math. Letters, Vol. 6, No. 5 (1993), 71-74; Math. Rev. Author index 1996.

125.      On an application of a variant of the closed graph theorem and the secant method, Tamkang J. Math., Vol. 24, No. 3 (1993), 251-267; Math. Rev. 94m:65098, Rabindra Nath Sen.

126.      Newton-like methods in partially ordered Banach spaces, Approx. Theory and Its Applic., 9:1 (1993), 1-9; Math. Rev. 94f:47086, Mihai Turinici

127.      Results on the Chebyshev method in Banach spaces, Proyecciones Revista, Vol. 12, No. 2 (1993), 119-128; Math. Rev. 94j:65078, A.M. Galperin (IL-BGUN; Be'er Sheva).

128.      On the convergence of an Euler-Chebysheff-type method under Newton-Kantorovich hypotheses, Pure Mathematics and Applications, Vol. 4, No. 3 (1993), 369-373; Math. Rev. 95g:65081, Tetsuro Yamamoto.

129.      A note on the Halley method in Banach spaces, Appl. Math. and Comp., 58 (1993), 215-224; Math. Rev. 94k:65082, Erich Bohl (Konstanz).

130.      On the solution of underdetermined systems of nonlinear equations in Euclidean spaces, Pure Mathematics and Applications, Vol. 4, No. 3 (1993), 199-209; Math. Rev. 95a:65089.

131.      On the a posteriori error bounds for a certain iteration under Zabrejko-Ngyen assumptions, Rev. Academia de Ciencias, Zaragoza, 48 (1993), 77-85; Math. Rev. 95b:65076.

132.      Newton-like methods in generalized Banach spaces, Functiones et Approximatio, XXII (1993), 107-114; Math. Rev. 95i:65088, Mihai Turinici.

133.      On S-order of convergence, Rev. Academia de Ciencias Zaragoza, 48 (1993), 69-76; Math. Rev. Author index 1994.

134.      A theorem on perturbed Newton-like methods in Banach spaces, Studia Scientiarum Mathematicarum Hungarica, 29 (1994), 295-305; Math. Rev. 95i:65089.

135.      Some notes on nonstationary multistep iteration processes, Acta Mathematica Hungarica, Vol. 64, 1 (1994), 59-64; Math. Rev. 94m:90098.

136.      Improved a posteriori error bounds for Zincenko's iteration, Intern. J. Comp. Math., Vol. 51 (1994), 51-54.

137.      The Jarratt method in a Banach space setting, J. Comp. Appl. Math., 51 (1994), 103-106; Math. Rev. 95c:65088.

138.      The midpoint method in Banach spaces and Ptak-error estimates, Appl. Math. and Computation, 62, 1 (1994), 1-15; Math. Rev. 95c:65087, Mihai Turinici.

139.      A convergence theorem for Newton-like methods under generalized Chen-Yamamoto-type assumptions, Appl. Math. and Comput., 61, 1 (1994), 25-37; Math. Rev. 65g:65082.

140.      On the convergence of some projection methods and inexact Newton-like iterations, Tamkang J. Math., Vol. 25, No. 4 (1994), 335-341; Math. Rev. 95m:65105, Mihai Turinici.

141.      On Newton's method and nonlinear operator equations, P.U.J.M., Vol. 27 (1994), 34-44; Math. Rev. Author index 1996.

142.      On the midpoint iterative method for solving nonlinear operator equations and applications to the solution of integral equations, Revue D'Analyse Numerique et de Theorie de l'Approximation, Tome 23, fasc. 2 (1994), 139-152; Math. Rev. 97j:65093.

143.      Parameter based algorithms for approximating local solutions of nonlinear complex equations, Proyecciones, Vol. 13, No. 1 (1994), 53-61; Math. Rev. 95f:65100.

144.      The Halley-Werner method in Banach spaces, Revue D'Analyse Numerique et de Theorie de l'Approximation, Tome 23, fasc. 2 (1994), 1-14; Math. Rev. 96c:65099, G. Alefeld (CD-KLRH-A; Karlsruhe).

145.      Error bound representations of Chebysheff-Halley-type methods in Banach spaces, Rev. Academia de Ciencias Zaragoza, 49 (1994), 57-69; Math. Rev. 95j:65065.

146.      On the discretization of Newton-like methods, Internat. J. Computer. Math., Vol. 52 (1994), 161-170.

147.      A local convergence theorem for the super-Halley method in a Banach space, Appl. Math. Lett., Vol. 7, No. 5 (1994), 49-52; Math. Rev. Author index 1996.

148.      A convergence analysis for a rational method with a parameter in Banach space, Pure Mathematics and Applications, 5, 1 (1994), 59-73; Math. Rev. 95j:65063.

149.      On sufficient conditions of the convergence and an optimality of error estimate for a high speed iterative algorithm for solving nonlinear algebraic systems, Chinese J. Math., Vol. 22, No. 4 (1994), 373-384; Math. Rev. 95i:65078, Xiaojun Chen.

150.      On the convergence of modified contractions, Journ. Comput. Appl. Math., 55, 2 (1994), 183-189; Math. Rev. 96a:65085.

151.      A multipoint Jarratt-Newton-type approximation algorithm for solving nonlinear operator equations in Banach spaces, Functiones et Aproximatio Commentarii Matematiki, XXIII (1994), 97-108; Math. Rev. 96c:65098.

152.      Convergence results for the super-Halley method using divided differences, Functiones et Approximatio Commentari Mathematici, XXIII (1994), 109-122; Math. Rev. 96d:6509.

153.      On the aposteriori error estimates for Stirling's method, Studia Scientiarum Mathematicarum Hungarica, 30, 3-4 (1995), 205-216; Math. Rev. 96g:65055, Otmar Scherzer (1-DE; Newark, DE).

154.      Sufficient conditions for the convergence of Newton-like methods under weak smoothness assumptions, Mathematics, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh Conference on Computational and Applied Mathematics (1995), 1-13; Mathematical Sciences Research Hot-Line, 5, 3 (2001), 17-27.

155.      On Stirling's method, Tamkang J. Math., Vol. 27, No. 1 (1995).

156.      Stirling's method and fixed points of nonlinear operator equations in Banach space, Bulletin of the Institute of Mathematics Academic Sinica, Vol. 23, No. 1 (1995), 13-20; Math. Rev. 96b:65060, A.M. Galperin (IL-BGUN; Be'er Sheva).

157.      Error bounds for fast two-point Newton methods of order four, Mathematics, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh Annual Conference on Computational and Applied Mathematics (1995), 14-18; Mathematical Sciences Research Hot-Line, 5, 3 (2001), 29-33.

158.      Improved error bounds for fast two-point Newton methods of order three, Mathematics, CAM 95, Edmond, OK (1995), Proceedings of the Eleventh Annual Conference on Computational and Applied Mathematics (1995), 19-23; Rev. Academia de Ciencias, Zaragoza, 50 (1995), 15-19; Math. Rev. Author index 1996.

159.      Stirling's method in generalized Banach spaces, Annales Univ. Sci. Budapest. Sect. Comp., 15 (1995), 37-47; Math. Rev. 97m:47093 (George Isac).

160.      A unified approach for constructing fast two-step Newton-like methods, Monatshefte fur Mathematik, 119 (1995), 1-22; Math. Rev. 96a:65093, Otmar Scherzer (1-TXAM; College Station, TX).

161.      On the Secant method and the Ptak error estimates, Revue d'Analyse Numerique et de Theorie de l'Approximation, 24, 1-2 (1995), 3-14; Math. Rev. 1998, pp. 58.

162.      An error analysis for the secant method under generalized Zabrejko-Nguen-type assumptions, Arabian Journal of Science and Engineering, 20:1 (1995), 197-206; Math. Rev. 96c:65100, A.M. Galperin (IL-BGUN; Be'er Sheva).

163.      Optimal-order parameter identification in solving nonlinear systems in a Banach space, Journal of Computational Mathematics, 13, 3 (1995), 267-280; Math. Rev. 96j:65070, A.A. Fonarev (Moscow).

164.      Nondifferentiable operator equations on Banach spaces with a convergence structure, Pure Mathematics and Applications, (PUMA), Vol. 6, 1 (1995), Math. Rev. 97h:47062.

165.      Perturbed Newton-like methods and nondifferentiable operator equations on Banach spaces with a convergence structure, (SWJPAM) Southwest Journal of Pure and Applied Mathematics, 1 (1995), 1-12; Math. Rev. 97k:65139, A.M. Galperin.

166.      Results on controlling the residuals of perturbed Newton-like methods on Banach spaces with a convergence structure, (SWJPAM) Southwest Journal of Pure and Applied Mathematics, 1 (1995), 32-38; Math. Rev. 97k:65140.

167.      A study on the order of convergence of a rational iteration for solving quadratic equations in a Banach space, Rev. Academia de Ciencias, Zaragoza, 50 (1995), 35-40; Math. Rev. Author index 1996.

168.      On an application of a variant of the closed graph theorem to the solution of nonlinear equations, Pure Mathematics and Applications, (PUMA), 6, 4 (1995), 301-312; Math. Rev. 97b:47063, M.Z. Nashed.

169.      Results on Newton methods; Part I: A unified approach for constructing perturbed Newton-like methods in Banach space and their applications, Appl. Math. and Comp., 74, 2-3 (1996), 119-141; Math. Rev. 97b:65074, De Ren Wang.

170.      Results on Newton methods; Part II: Perturbed Newton-like methods in generalized Banach spaces, Appl. Math. and Comp., 74, 2-3 (1996), Math. Rev. 97b:65075, De Ren Wang.

171.      On the method of tangent hyperbolas, Journal of Approximation Theory and Its Applications, 12, 1 (1996), 78-95, Math. Reviews AMS 99d65174.

172.      A unified approach for constructing fast two-step methods in Banach space and their applications, Proc. 12th Conference CAM 96, Computational and Applied Math., Edmond, OK, (1996), 1-50; Pan American Math. J., 13, 3 (2003), 59-108.

173.      On the method of tangent parabolas, Functiones et Approximatio Commentarii Mathematici, XXIV (1996), 3-15; Math. Rev. 98a:65077.

174.      On an extension of the mesh-independence principle for operator equations in Banach space, Appl. Math. Lett., Vol. 9, No. 3 (1996), 1-7; Math. Rev. 97a:47108.

175.      An inverse-free Jarratt type approximation in a Banach space, Journal of Approximation Theory and Its Applications, 12, 1 (1996), 19-30; Math Rev. 1998, pp. 58.

176.      An error analysis for the Steffensen method under generalized Zabrejko-Nguen-type assumptions, Revue d'Analyse Numérique et de Théorie de l'Approximation, 25, 1-2 (1996), 11-22; Math. Reviews AMS Gabriel Dimitriu 99c47105.

177.      Concerning the convergence of inexact Newton-like methods on Banach spaces with a convergence structure and applications, Proceedings of the International Conference on Approximation and Optimization (Romania) - ICAOR Cluj-Napoca, July 19-August 1, (1996), 163-172; Math. Rev. 98j:65040.

178.      Improved error bounds for an Euler-Chebysheff-type method, Pure Math. Appl. (PUMA), 7, 1-2 (1996), 41-51; Math. Rev. 97j:65097.

179.      On the convergence of perturbed Newton-like methods in Banach space and applications, Southwest J. Pure Appl. Math., 2 (1996), 34-41; Math Rev. 98b:65060.

180.      Sufficient conditions for the convergence of iterations to points of attraction in Banach spaces, Southwest J. Pure Appl. Math., 2 (1996), 42-47; Math. Rev. 98b:65061.

181.      Weak conditions for the convergence of iterations to solutions of equations on partially ordered topological spaces, Southwest J. Pure Appl. Math., 2 (1996), 48-54; Math Rev. 98b:65062.

182.      On the monotone convergence of implicit Newton-like methods, Southwest J. Pure Appl. Math., 2 (1996), 55-59; Math Rev. 98b:65063.

183.      A generalization of Edelstein's theorem on fixed points and applications, Southwest J. Pure Appl. Math., 2 (1996), 60-64; Math. Rev. 98a:65078.

184.      Generalized conditions for the convergence of inexact Newton methods on Banach spaces with a convergence structure and applications, Pure Mathematics and Applications (PUMA), 7, 3-4 (1996), 197-214; Math. Rev. Author index 1997.

185.      Error bounds for an almost fourth order method under generalized conditions, Rev. Academia de Ciencias, Zaragoza, 51 (1996), 19-26; Math. Rev. 98c:65091, Tetsuro Yamamoto.

186.      A simplified proof concerning the convergence and error bound for a rational cubic method in Banach spaces and applications to nonlinear integral equations, Rev. Academia de Ciencias, Zaragoza, 51 (1996), 47-55; Math. Rev. 98e:65074, Xiaojun Chen.

187.      On the convergence of Chebysheff-Halley-type method using divided differences of order one, Rev. Academia de Ciencias, Zaragoza, 51 (1996), 27-45; Math. Rev. 98d:65074.

188.      On the convergence of two-step methods generated by point-to-point operators, Appl. Math. and Comput., 82, 1 (1997), 85-96; Math. Rev. 97m:65107, A.M. Galperin, Boro Doring.

189.      Improved error bounds for Newton-like iterations under Chen-Yamamoto assumptions, Appl. Math. Lett., 10, 4 (1997), 97-100; Math. Rev. 1998, pp. 59.

190.      Inexact Newton methods and nondifferentiable operator equations on Banach spaces with a convergence structure, Approx. Th. Applic., 13, 3 (1997), 91-104; Math. Reviews AMS 99a47101.

191.      A mesh independence principle for inexact Newton-like methods and their discretizations under generalized Lipschitz conditions, Appl. Math. Comp., 87 (1997), 15-48; Math. Rev. 98d:65075, Asen L. Dontchev.

192.      On the super-Halley method using divided differences, Appl. Math. Lett., 10, 4 (1997), 91-95; Math. Rev. 1998, pp. 59.

193.      Chebysheff-Halley like methods in Banach spaces, Korean Journ. Comp. Appl. Math., Vol. 4, No. 1 (1997), 83-107; Math. Rev. 98a:47068, Tetsuro Yamamoto.

194.      Concerning the convergence of inexact Newton methods, J. Comp. Appl. Math., 79 (1997), 235-247; Math. Rev. 98c:47077, P.P. Zabrejko.

195.      General ways of constructing accelerating Newton-like iterations on partially ordered topological spaces, Southwest Journal of Pure and Applied Mathematics, 1 (1997), 18-22; Math. Rev. AMS 99d65176.

196.      Smoothness and perturbed Newton-like methods, Pure Mathematics and Applications (PUMA), 8, 1 (1997), 13-28; Math. Rev. 98h:65023.

197.      A mesh independence principle for operator equations and Steffensen-method, Korean J. Comp. Appl. Math., 4, 2 (1997), 263-280; Math. Rev. 98c:65092.

198.      Improving the rate of convergence of Newton methods on Banach spaces with a convergence structure and applications, Appl. Math. Lett., 10, 6 (1997), 21-28; Math. Rev. 1999, pp. 59.

199.      A new convergence theorem for Steffensen's method on Banach spaces and applications, Southwest Journal of Pure and Applied Mathematics, 1 (1997), 23-29; Math. Rev. AMS 99d65177.

200.      A local convergence theorem for the inexact Newton method at singular points, Southwest Journal of Pure and Applied Mathematics, 1 (1997), 30-36; Math. Rev. AMS 99d65178.

201.      Applications of a special representation of analytic functions, Southwest Journal of Pure and Applied Mathematics, 2 (December 1997), 43-47; Math. Rev. AMS 99h65101 (John G. Stalker).

202.      On a new Newton-Mysovskii-type theorem with applications to inexact Newton-like methods and their discretizations, IMA J. Num. Anal., Journal of the Institute of Mathematics and Its Applications, 18 (1997), 37-56; Math. Rev. AMS 99a65075 (De Ren Wang).

203.      Results involving nondifferentiable equations on Banach spaces with a convergence structure and Newton methods, Rev. Academia de Ciencias, de Zaragoza, 52 (1997), 23-30; Math. Rev. AMS 99c57101 (A.M. Galperin).

204.      The asymptotic mesh independence principle for inexact Newton-Galerkin-like methods, PUMA, 8, 2-3-4, (1997), 169-194; Math. Rev. AMS 99d65175

205.      The Halley method in Banach spaces and the Ptak error estimates, Rev. Academia de Ciencias, de Zaragoza, 52 (1997), 31-41; Math. Rev. AMS 99c47108 (A.M. Gulperin).

206.      Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton's method, Southwest J. Pure Appl. Math., 1 (1998), 24-28; Math. Rev. AMS 99d65180.

207.      On the monotone convergence of an Euler-Chebysheff-type method in partially ordered topological spaces, Revue d'Analyse Numerique et de Theorie de l'Approximation, 27, 1 (1998), 23-31.

208.      Sufficient conditions for constructing methods faster than Newton's, Appl. Math. Comp., 93 (1998), 169-181; Math. Rev. AMS 99c65110.

209.      Error bounds for the Chebyshev method in Banach spaces, Bull. Inst. Acad. Sinica, 26, 4 (1998), 269-282; Math. Rev. AMS 99h65118.

210.      Improving the rate of convergence of some Newton-like methods for the solution of nonlinear equations containing a nondifferentiable term, Revue d'Analyse Numerique et de Theorie de l'Approximation, 27, 2 (1998), 191-202.

211.      On the convergence of a certain class of iterative procedures under relaxed conditions with applications, J. Comp. Appl. Math., 94 (1998), 13-21; Math. Rev. AMS 99d65179.

212.      Improving the order and rates of convergence for the Super-Halley method in Banach spaces, Korean J. Comp. Appl. Math., 5, 2 (1998), 465-474; Math. Rev. AMS 99f65083 (A.M. Galperin).

213.      A new convergence theorem for the Jarratt method in Banach spaces, Computers and Mathematics with Applications, 36, 8 (1998), 13-18; Math. Rev. AMS 99g65066.

214.      Generalized conditions for the convergence of inexact Newton-like methods on Banach spaces with a convergence structure and applications, Korean J. Comp. Math., 5, 2 (1998), 391-405.

215.      On Newton's method under mild differentiability conditions and applications, Appl. Math. Comp., 102 (1999), 177-183; Math. Rev. AMS Annual Author Index 1999.

216.      Improved error bounds for a Chebysheff-Halley-type method, Acta Math. Hungarica, 84, (3) (1999), 209-219.

217.      Convergence rates for inexact Newton-like methods at singular points and applications, Appl. Math. Comp., 102 (1999), 185-201; Math. Rev. AMS Annual Author Index 1999.

218.      Convergence domains for some iterative processes in Banach spaces using outer and generalized inverses, J. Computational Analysis and Applications, Vol. 1, No. 1, (1999), 87-104.

219.      Concerning the convergence of a modified Newton-like method, Zeitschrift fur analysis und ihre Anwendungen, Journal for Analysis and Applications, 18, (3) (1999), 785-792.

220.      A new convergence theorem for Newton-like methods in Banach space and applications, Comput. Appl. Math., 18, 3 (1999), 343-353

221.      A new convergence theorem for inexact Newton methods based on assumptions involving the second Frechet-derivative, Computers and Mathematics with Applications, 37 (1999), 109-115.

222.      The Halley-Werner method in Banach spaces and the Ptak error estimates, Bulletin Hong-Kong Math. Soc. BHKMS, Vol. 2 (1999), 357-371.

223.      Concerning the radius of convergence of Newton's method and applications, Korean J. Comp. Appl. Math., Vol. 6, No. 3 (1999), 451-462.

224.      Relations between forcing sequences and inexact-Newton-like iterates in Banach space, Intern. J. Comp. Math., 71 (1999), 235-246.

225.      On the applicability of two Newton methods for solving equations in Banach space, Korean J. Comp. Appl. Math., Vol. 6, No. 2 (1999), 267-275; Math. Rev. AMS Annual Author Index 1999.

226.      Affine invariant local convergence theorems for inexact Newton-like methods, Korean J. Comp. Appl. Math., Vol. 6, No. 2 (1999), 291-304; Math. Rev. AMS Annual Author Index 1999,

227.      A convergence analysis for Newton-like methods in Banach space under weak hypotheses and applications, Tamkang J. Math., Vol. 30, No. 4 (1999), 253-261.

228.      An error analysis for the midpoint method, Tamkang J. Math., Vol. 30, No. 2 (1999), 71-83.

229.      Approximating solutions of operator equations using modified contractions and applications, Studia Scientiarum Mathematicarum Hungarica, 35 (1999), 207-215.

230.      Convergence results for a fast iterative method in linear spaces, Taiwanese J. Math., 3, (1999), 323-338.

231.      A generalization of Ostrowski's theorem on fixed points, Appl. Math. Letters, 12 (1999), 77-79.

232.      A new Kantorovich-type theorem for Newton's method, Applicationes Mathematicae, 26, 2 (1999), 151-157.

233.      A monotone convergence theorem for Newton-like methods using divided differences of order two, Southwest J. Pure Appl. Math., 1 (1999).

234.      On the convergence of Newton's method for polynomial equations and applications in radiative transfer, Monatschefte fur Mathematik, 27 (1999), 265-276.

235.      On the convergence of Steffensen-Aitken-like methods using divided differences obtained recursively, Rev. Anal. Numer. Theor. Approx., 28, 2 (1999), 109-117.

236.      Local and global convergence results for a class of Steffensen-Aitken-type methods, Adv. Nonlinear Var. Ineq., 2, 2 (1999), 117-126.

237.      Relations between forcing sequences and inexact Newton iterates in Banach space, Computing, 63 (1999), 131-144.

238.      A new convergence theorem for the method of tangent hyperbolas in Banach space, Proyecciones, 18, 1 (1999), 1-11.

239.      Local convergence of inexact Newton methods under affine invariant conditions and hypotheses on the second Frechet-derivative, Applicationes Mathematicae, 26, 4 (1999), 457-465.

240.      Convergence theorems for some variants of Newton's method of order greater than two, Punjab. Univ. J. Math., XXXII (1999), 93-98.

241.      Accessibility of solutions of equations on Banach spaces by a Stirling-like method, Rev. Acad. de Ciencias Zaragoza, 54 (1999), 93-98.

242.      Newton methods on Banach spaces with a convergence structure and applications, Computers and Math. with Appl., Intern. J., Pergamon Press, 40, 1 (2000), 37-48.

243.      Accessibility of solutions of equations on Banach spaces by Newton-like methods and applications, Bulletin Inst. Math. Acad. Sinica, Vol. 28, No. 1 (2000), 9-20.

244.      Forcing sequences and inexact Newton iterates in Banach space, Appl. Math. Letters, 13 (2000), 77-80.

245.      Choosing the forcing sequences for inexact Newton methods in Banach space, Comput. Appl. Math., 19, 1 (2000), 79-89.

246.      Conditions for the convergence of perturbed Steffensen methods on a Banach space with a convergence structure, Adv. Nonlinear Var. Inequal, 3, 1 (2000), 23-35.

247.      On some general iterative methods for solving nonlinear operator equations containing a nondifferentiable term, Adv. Nonlinear Var. Inequal., 3, 1 (2000), 15-21.

248.      A mesh independence principle for perturbed Newton-like methods and their discretizations, Korean J. Comp. Appl. Math., 7, 1 (2000), 139-159.

249.      A convergence theorem for Newton-like methods in Banach space under general weak assumptions and applications, Communications on Applied Analysis, 7, 2 (2000), 57-72.

250.      Error bounds for the Halley-Werner method in Banach spaces, Communications on Applied Nonlinear Analysis, 7, 2 (2000), 73-85.

251.      Extending the region of convergence for a certain class of modified iterative methods on Banach space and applications, Adv. Nonlinear Var. Inequalities, 3, 1 (2000), 1-5.

252.      Improved error bounds for Newton's method under hypotheses on the second Frechet-derivative, Adv. Nonlinear Var. Inequal., 3, 1 (2000), 37-45.

253.      Local convergence of inexact Newton-like iterative methods and applications, Computers and Mathematics with Applications, 39 (2000), 69-75.

254.      A unifying semilocal convergence theorem for Newton-like methods in Banach space, Pan American Mathematical Journal, 10, 1 (2000), 95-101.

255.      Perturbed Steffensen-Aitken projection methods for solving equations with nondifferentiable operators, PUNJAB J. Math., 33 (2000), 105-113.

256.      Semilocal convergence theorems for a certain class of iterative procedures using outer or generalized inverses, Korean J. Comp. Appl. Math., 7 1 (2000), 29-40.

257.      Improving the order of convergence of Newton's method for a certain class of polynomial equations, SooChow J. Math., 26, 2 (2000), 117-122.

258.      On the convergence of Steffensen-Galerkin methods, Atti del seminario Matematica e Fisico dell'universita di Modena, XLVIII, 11 (2000), 355-370.

259.      A convergence theorem for Newton's method under uniform-like continuity conditions on the second Frechet-derivative, Atti del seminario Matematica e Fisico dell'universita di Modena, XLVIII (2000), 235-243.

260.      A new convergence theorem for Stirling's method in Banach space, Atti del seminario Matematicae Fisico dell'universita di Modena, XLVIII (2000), 225-233.

261.      The Steffensen method on special Banach spaces, Communications on Applied Nonlinear Analysis, 7, 4 (2000), 49-58.

262.      A new convergence theorem for the Steffensen method in Banach space and applications, Rev. Anal. Numer. Theor. Approx., 29, 2 (2000), 119-127.

263.      The Chebyshev method in Banach spaces and the Ptak error estimates, Advances in Nonlinear Variational Inequalities, 3, 2 (2000), 15-25.

264.      A convergence theorem for Steffensen's method and the Ptak error estimates, Advances in Nonlinear Variational Inequalities, 3, 2 (2000), 43-51.

265.      Iterative methods for order between 1.618... and 1.839..., Communications on Applied Nonlinear Analysis, 7, 4 (2000), 59-70.

266.      Convergence theorems for Newton-like methods under generalized Newton-Kantorovich conditions, Advances in Nonlinear Inequalities, 3, 2 (2000), 35-42.

267.      On the local convergence of m-step Newton methods with applications on a vector supercomputer, Advances in Nonlinear Inequalities, 3, 2 (2000), 27-33.

268.      Concerning the monotone convergence of the method of tangent hyperbolas, Korean J. Comp. Appl. Math., 7, 2 (2000), 407-418.

269.      On the convergence of an Euler-Chebysheff-type method using divided differences of order one, Communications on Applied Nonlinear Analysis, 7, 4 (2000), 71-86.

270.      On the convergence of disturbed Newton-like methods in Banach space, Pan American Mathematical Journal, 10(3) (2000), 31-39.

271.      Error bounds for the Halley method in Banach spaces, Advances in Nonlinear Variational Inequalities, 3(2) (2000), 1-13.

272.      Improving the rate of convergence of Newton-like methods in Banach space using twice Frechet-differentiable operators and applications, Pan American Mathematical Journal, 10(3) (2000), 51-59.

273.      The effect of rounding errors on a certain class of iterative methods, Applicationes Mathematicae, 27, 3 (2000), 369-375.

274.      Semilocal convergence theorems for Newton's method using outer inverses and hypotheses on the mth Frechet-derivative, Mathematical Sciences Research Hot-Line, 4, 5 (2000), 33-45.

275.      Convergence results for Newton's method involving smooth operators, Mathematical Sciences Research Hot-Line, 4, 5 (2000), 35-43.

276.      The effect of rounding errors on Newton methods, Korean J. Comp. Appl. Math., 7, 3 (2000), 533-540.

277.      Local convergence theorems of Newton's method for nonlinear equations using outer or generalized inverses, Chechoslovak Math. J., 50(125) (2000), 603-614.

278.      On the monotone convergence of a Chebysheff-Halley-type method in partially ordered topological spaces, Annales Univ. Sci. Budapest. Sect. Comp., 19 (2000), 143-154.

279.      Forcing sequences and inexact iterates involving m-Frechet differentiable operators, Mathematical Sciences Research Hot-Line, 4, 9 (2000), 35-46; MR 2001K: 65095.

280.      Local convergence of a certain class of iterative methods and applications, Mathematical Sciences Research Hot-Line, 4, 11 (2000), 9-16.

281.      A new semilocal convergence theorem for Newton's method using hypotheses on the m-Frechet derivative, Mathematical Sciences Research Hot-Line, 4, 8 (2000), 57-61.

282.      Choosing the forcing sequences for inexact Newton methods and m-Frechet differentiable operators, Mathematical Sciences Research Hot-Line, 4, 11 (2000), 1-8.

283.      Semilocal convergence theorems for a certain class of iterative procedures involving m-Frechet differentiable operators, Mathematical Sciences Research Hot-Line, 4, 8 (2000), 1-12.

284.      Local convergence theorems for Newton's method using outer or generalized inverses and m-Frechet differentiable operators, Mathematical Sciences Research Hot-Line, 4, 8 (2000), 47-56.

285.      Relaxing convergence conditions of Newton-like methods for solving equations under weakened assumptions, Mathematical Sciences Research Hot-Line, 4, 7 (2000), 55-64.

286.      Convergence domains of Newton-like methods for solving equations under weakened assumptions, Mathematical Sciences Research Hot-Line, 4, 7 (2000), 64-73.

287.      Approximation-solvability of nonlinear variational inequalities and partially relaxed monotone mappings, Communications on Applied Nonlinear Analysis, 7(4) (2000), 1-10.

288.      On a class of nonlinear implicit quasivariational inequalities, Pan American Math. J., 10, 4 (2000), 101-109.

289.      Convergence theorems for Newton's method without Lipschitz conditions and hypotheses on the first Frechet-derivative, Mathematical Sciences Research Hot-Line, 4, 11 (2000), 41-50.

290.      Enlarging the radius of convergence for Newton's method, Mathematical Sciences Research Hot-line, 4, 11 (2000), 29-40.

291.      Semilocal convergence theorems for Newton's method using outer inverses and no Lipschitz conditions, Mathematical Sciences Research Hot-Line, 4, 11 (2000), 59-68.

292.      Local convergence theorems for Newton's method using outer or generalized inverses and no Lipschitz conditions, Mathematical Sciences Research Hot-Line, 4, 12 (2000), 1-11.

293.      A mesh independence principle for Newton's method using twice Frechet-differentiable operators, Mathematical Sciences Research Hot-Line, 4, 11 (2000), 17-27.

294.      The asymptotic mesh independence principle for Newton-Galerkin methods using weak hypotheses on the Frechet derivatives, Mathematical Sciences Research Hot-Line, 4, 11 (2000), 51-58.

295.      On the approximate solution of implicit functions using the Steffensen method, Proyecciones revista de matematica, 19, 3 (2000), 291-303.

296.      Approximate solutions of equations by a Stirling method, Bulletin Institute Academia Sinica, 28, 4 (2000), 249-256.

297.      Inexact Steffensen-Aitken methods for solving equations, Pan American Mathematical Journal, 10, 4 (2000), 71-75.

298.      An error analysis for Steffensen's method, Pan American Mathematical Journal, 11, 1 (2000), 91-96.

299.      Convergence results for nonlinear equations under generalized Holder continuity assumptions, Communications on Applied Nonlinear Analysis, 7, (2) (2000), 57-72.

300.      A fixed point theorem for perturbed Newton-like methods on Banach spaces and applications to the solution of nonlinear integral equations appearing in radiative transfer, Communications in Applied Analysis, 4, 3 (2000), 297-303.

301.      On multilinear equations, Mathematical Sciences Research Hot-Line, 5, 3 (2001), 53-63.

302.      On a new iteration for solving the Chandrasekhar's H-equations, Mathematical Sciences Research Hot-Line, 5, 3 (2001), 35-42.

303.      On a generalization of fixed and common fixed point theorems of operators in complete metric spaces, Mathematical Sciences Research Hot-Line, 5, 3 (2001), 43-51.

304.      An algorithm for solving nonlinear programming problems using Karmarkar's technique, Mathematical Sciences Research Hot-Line, 5, 4 (2001), 59-67.

305.      On an application of a modification of a Newton-like method to the approximation of implicit functions, Mathematical Sciences Research Hot-Line, 5, 6 (2001), 1-10.

306.      On the monotone convergence of fast iterative methods in partially ordered topological spaces, Mathematical Sciences Research Hot-Line, 5, 3 (2001), 13-16.

307.      A new semilocal convergence theorem for Newton's method in Banach space using hypotheses on the second Frechet-derivative, Journal of Comput. Appl. Math., 139 (2001), 369-373.

308.      On the radius of convergence of Newton's method, Internat. Journ. Computer Math., Vol. 77, 3 (2001), 389-400.

309.      Error bounds for Newton's method under hypotheses on the mth Frechet-derivative, Advances in Nonlinear Variational Inequalities, 4, 1 (2001), 23-33.

310.      A modification of the Newton-Kantorovich hypotheses for the convergence of Newton's method, Advances in Nonlinear Variational Inequalities, 4(1) (2001), 35-40.

311.      Local and semilocal convergence theorems for Newton's method based on continuously Frechet-differentiable operators, Southwest Journal of Pure and Applied Mathematics, 1 (2001), 22-28.

312.      Steffensen-Aitken-type methods and implicit functions, Pan American Mathematical Journal, 11, 1 (2001), 91-96.

313.      On controlling the residuals of some iterative methods, Communications on Applied Nonlinear Analysis, 8, 2 (2001), 67-72.

314.      Error bounds for the midpoint method in Banach spaces, Communications on Applied Nonlinear Analysis, 8, 3 (2001), 103-117.

315.      Enlarging the region of convergence for a certain iterative method, Pan American Mathematical Journal, 11, 1 (2001), 83-89.

316.      A new convergence theorem for the method of tangent parabolas in Banach space, Pan American Mathematical Journal, 11, 1 (2001), 75-81.

317.      Semilocal convergence results for Newton-like methods using Kantorovich quasi-majorant functions involving the first derivative, Commun. Appl. Nonlin. Anal., 8, 1 (2001), 79-87.

318.      Local convergence theorems for Newton methods, Korean J. Comp. Appl. Math. 8, 2 (2001), 253-268.

319.      On the local convergence of m-step Newton methods and J-Frechet differentiable operators with applications on a vector super computer, Communications on Applied Nonlinear Analysis, 8, 1 (2001), 97-104.

320.      A new convergence theorem for the secant method in Banach space and applications, Communications on Applied Nonlinear Analysis, 8, 1 (2001), 89-95.

321.      A Newton-Kantorovich theorem for equations involving m-Frechet differentiable operators and applications in radiative transfer, Journ. Comp. Appl. Math., 131, 1-2 (2001), 149-159.

322.      On a new method for enlarging the radius of convergence for Newton's method, Applicationes Mathematicae, 28, 1 (2001), 1-15.

323.      Relations between forcing sequences and inexact Newton iterates involving m-Frechet derivatives, Mathematical Sciences Research Hot-Line, 5, 11 (2001), 1-11.

324.      Semilocal convergence theorems for Newton's method using outer inverses and hypotheses on the second Frechet-derivative, Monatshefte fur Mathematik, 132 (2001), 183-195.

325.      On general auxiliary problem principle and nonlinear mixed variational inequalities, Nonlinear Functional Analysis and Applications, 6, 2 (2001), 247-256.

326.      A mesh independence principle for Newton's method without Lipschitz conditions on the second Frechet-derivative, Pan American Mathematical Journal, 11, 3 (2001), 99-107.

327.      An error analysis for a certain class of iterative methods, Korean J. of Comput. and Appl. Math., 8, 3 (2001), 519-529.

328.      On an iterative procedure for approximating solutions of quasi variational inequalities, Advances in Nonlinear Variational Inequalities, 4, 2 (2001), 39-42.

329.      On generalized variational inequalities, Advances in Nonlinear Variational Inequalities, 4, 2 (2001), 75-78.

330.      On a semilocal convergence theorem for a class of quasi variational inequalities, Advances in Nonlinear Inequalities, 4, 2 (2001), 43-46.

331.      On the convergence of a certain class of iterative methods and applications in neutron transport, Mathematical Sciences Research Hot-Line, 5, 5 (2001), 1-13.

332.      Semilocal convergence of the secant method under relaxed conditions and applications, Mathematical Sciences Research Hot-Line, 5, 12 (2001), 1-9.

333.      A mesh independence principle for inexact Newton-type methods and their discretizations, Annales Univ. Sci. Budapest, Sect. Comp., 20 (2001), 31-53.

334.      Convergence theorems for Newton-like methods using data from a set or a single point and outer inverses, Southwest J. Pure Appl. Math., 2 (2001), 19-23.

335.      The secant method under weak assumptions, Communications in Applied Nonlinear Analysis, 9, 4 (2002), 115-126.

336.      Perturbed Newton methods in generalized Banach spaces, Commun. in Appl. Anal., 6, 2 (2002), 241-258.

337.      On the radius of convergence of Newton-like methods, Communications in Applied Analysis, 6/7 (2002), 527-534.

338.      Convergence domains for some iterative procedures in Banach spaces, Communications on Applied Analysis, 6, 4 (2002), 515-526.

339.      A semilocal convergence theorem for inexact Newton methods involving m-Frechet derivatives, Pan American Mathematical Journal, 12, (3) (2002), 73-83.

340.      Local convergence of iterative methods under affine invariant conditions and hypotheses on the mth Frechet-derivative, Pan American Math. J., 12, 1 (2002), 11-21.

341.      A unifying semilocal convergence theorem for a certain class of iterative methods under weak conditions and applications, Advances in Nonlinear Variational Inequalities, 5, 1 (2002), 51-56.

342.      Convergence theorems for Newton-like methods without Lipschitz conditions, Communications on Applied Nonlinear Analysis, 9, (3) (2002), 69-78.

343.      Convergence theorems for Newton's method without Lipschitz conditions and hypotheses on the m-Frechet derivative (m > 2), Pan American Mathematical Journal, 12, 1 (2002), 51-58.

344.      A mesh independence principle for Newton's method using center Lipschitz conditions on the second Frechet derivative, Communications on Applied Nonlinear Analysis, 9, (3) (2002), 69-78.

345.      Relations between Newton's method and its discretizations without Lipschitz conditions, Pan American Mathematical Journal, 12, 1 (2002), 95-99.

346.      Relations between Newton's method and its discretizations using center Lipschitz conditions, Communications on Applied Nonlinear Analysis, 9, 4 (2002), 61-66.

347.      The asymptotic mesh independence principle for Newton-Galerkin methods using twice Frechet-differentiable operators, Pan American Mathematical Journal, 12, 1 (2002), 85-93.

348.      The asymptotic mesh independence principle for Newton-Galerkin methods using twice Frechet-differentiable operators without Lipschitz conditions, Communications on Applied Nonlinear Analysis, 9, 4 (2002), 67-75.

349.      Convergence theorems for solving variational inequalities using the generalized Newton's method, Advances in Nonlinear Variational Inequalities, 5, 1 (2002), 43-49.

350.      Semilocal convergence theorems for solving variational inequalities, Advances in Nonlinear Variational Inequalities, 5, 1 (2002), 29-34.

351.      On the solution of generalized equations in a Hilbert space, Advances in Nonlinear Variational Inequalities, 5, 1 (2002), 35-41.

352.      On the solution of generalized equations using uniformly continuous operators and Kantorovich quasi-majorants, Advances in Nonlinear Variational Inequalities, 5, 1 (2002), 63-68.

353.      On the solution of generalized equations using mth (m > 2) Frechet differentiable operators, Communications on Appl. Non. Anal., 9, 1 (2002), 85-89.

354.      On the monotone convergence of the method of tangent hyperbolas, Pan American Math. J., 12, 1 (2002), 33-41.

355.      Approximate solution of linearized equations in a Banach space, Pan American Math. J., 12, 4 (2002), 55-59.

356.      Results on the solution of generalized equations, Commun. Appl. Nonlin. Anal., 9, 1 (2002), 103-107.

357.      On the solution of compact operator equations using the modified Newton's method with perturbation, Advances in Nonlinear Variational Inequalities, 5, 1 (2002), 57-61.

358.      On the solution of nonlinear equations under Holder continuity assumptions, Commun. in Appl. Anal., 6, 2 (2002), 259-272.

359.      On the convergence of a Newton-like method based on m-Frechet differentiable operators and applications in radiative transfer, Journal of Computational Analysis and Applications, 4, 2 (2002), 141-154.

360.      A unifying semilocal convergence theorem for Newton-like methods based on center Lipschitz conditions, Comput. Appl. Math., 21, 3 (2002), 789-796.

361.      On the convergence of Newton-like methods for analytic operators and applications, Journ. Appl. Math. and Computing, 10, 1-2 (2002), 41-50.

362.      Convergence of Stirling's method in Banach spaces and analytic operators, Math. Sc. Res. J., 6, 2 (2002), 92-95.

363.      A new theorem for computing fixed points, Math. Sc. Res. J., 6, 2 (2002), 78-83.

364.      New unifying convergence criteria for Newton-like methods, Applicationes Mathematicae, 29, 3 (2002), 359-369.

365.      Error bounds for Newton's method under a weak Kantorovich-type hypothesis, Southwest J. Pure Appl. Math., 2 (2002), 32-37.

366.      On the convergence of Steffensen-Galerkin-type methods in Banach space, Annales Univ. Sci. Budapest. Sect. Comp., 21 (2002), 3-18.

367.      Concerning the approximate solution of linearized equations, Math. Sci. Res. J., 6, 5 (2002),  234-240.

368.      Generalized partial relaxed monotonicity and solvability of nonlinear variational inequalities, Pan American Math. J., 12, 3 (2002), 73-83.

369.      Local convergence theorems for Newton's method from data at one point, Applicationes Mathematicae, 29, 4 (2002), 481-486.

370.      Approximate solution of linearized equations in a Hilbert space, Pan American Math. J., 13, 4 (2003), 55-60.

371.      A semilocal convergence analysis for the method of tangent hyperbolas, Journal of Concrete and Applicable Analysis, 1, 2 (2003), 137-150.

372.      New and generalized convergence conditions for the Newton-Kantorovich method, J. Appl. Anal., 9, 2 (2003),287-299.

373.      On the convergence and application of Newton's method under weak Holder continuity assumptions, International Journal of Computer Mathematics, 80, 5 (2003), 767-780.

374.      On a theorem of L.V. Kantorovich concerning Newton's method, Journ. Comp. Appl. Math., 155 (2003), 223-230.

375.      On the convergence of Newton's method for analytic operators, Southwest J. Pure Appl. Math., 1 (2003), 1-9.

376.      A unifying theorem on Newton's method in a Banach space with a convergence structure under weak assumptions, Southwest J. Pure Appl. Math., 1 (2003), 56-65.

377.      Semilocal convergence for Newton's method on a Banach space with a convergence structure and twice Frechet-differentiable operators, Southwest J. Pure Appl. Math., 1 (2003), 88-95.

378.      On some nonlinear equations, Advances in Nonlinear Variational Inequalities, 6 (2003), 75-80.

379.      On the approximation of solutions of compact operator equations, Advances in Nonlinear Variational Inequalities, 6, 2 (2003), 137-150.

380.      Approximating distinct solutions of quadratic equations in Banach space, Advances in Nonlinear Variational Inequalities, 6 (2003), 81-103.

381.      On a multistep Newton method in Banach spaces and the Ptak error estimates, Advances in Nonlinear Variational Inequalities, 6, 2 (2003), 121-135.

382.      On the convergence and application of Stirling's method, Applicationes Mathematicae, 30, 1 (2003), 109-119.

383.      A local convergence analysis and applications of Newton's method under weak assumptions, Southwest J. Pure Appl. Math., 1 (2003), 82-87.

384.      A convergence analysis and applications of Newton's method on generalized Banach spaces, Advances in Nonlinear Variational Inequalities, 6, 2 (2003), 109-119.

385.      On an application of a fixed point theorem to the convergence of inexact Newton-like methods, Communications on Applied Nonlinear Analysis, 10, 1 (2003), 101-108.

386.      Generalized conditions for the convergence of inexact Newton-like methods on Banach spaces with a convergence structure, Communications on Applied Nonlinear Analysis, 10, 1 (2003), 109-120.

387.      An improved error analysis for Newton-like methods under generalized conditions, J. Comput. Appl. Math., 157, 1, (2003), 169-185.

388.      An improved convergence analysis and applications for Newton-like methods in Banach space, Numerical Functional Analysis and Optimization, 24, 7&8, (2003), 653-672.

389.      A convergence analysis for Newton's method based on Lipschitz, center-Lipschitz conditions and analytic operators, Pan American Math. J., 13, 3, (2003), 19-24.

390.      Concerning the convergence of Newton-like methods under weak Holder continuity assumptions, Functiones et Approximatio, XXXI, (2003), 7-22.

391.      A convergence analysis of an iterative algorithm of order 1.839... under weak assumptions, Rev. Anal. Numer. Theor. Approx., 32, 2, (2003), 123-134.

392.      On the convergence and application of generalized Newton methods, Nonlinear Studies, 10, 4, (2003), 307-322.

393.      Concerning a local convergence theory for inexact-Newton methods, Pan American Mathematical Journal, 13, 4, (2003), 77-82.

394.      On an improved variant of the L.V. Kantorovich theorem for Newton's method, Mat. Sci. Res. J., 7, 10, (2003), 400-405.

395.      Concerning the convergence of Newton's method and logarithmic convexity, Pan American Mathematical Journal, 13, 3 (2003), 35-42.

396.      On the convergence of Newton-like methods using quasicontractive operators, Advances in Nonlinear Variational Inequalities, 7, 2 (2004), 71-78.

397.      Weak sufficient convergence conditions and applications for Newton-like methods, J. Appl. Math. Comput., 16, 1-2, (2004), 1-17.

398.      A unifying local-semilocal convergence analysis and applications for two point Newton-like methods in Banach space, Journal of Mathematical Analysis and Applications, 298, 2 (2004), 374-397.

399.      On the different convergence radii for Newton-like approximations, Advances in Nonlinear Variational Inequalities, 7, 2 (2004), 89-100.

400.      Local-semilocal convergence theorems for Newton's method in Banach space and applications, Advances in Nonlinear Variational Inequalities, 7, 1 (2004), 121-132.

401.      On the Newton-Kantorovich hypothesis for solving equations, J. Comput. Appl. Math., 169, (2004), 315-332.

402.      Concerning the convergence and application of Newton's method under hypotheses on the first and second Frechet-derivative, Communications in Applied Nonlinear Analysis, 11, 1, (2004), 103-110.

403.      On the convergence of a certain class of Steffensen iterative methods for solving equations, Math. Sci. Res. J., 8, 2, (2004), 55-66.

404.      A convergence analysis and applications of Newton-like methods under generalized Chen-Yamamoto-type assumptions, Intern. J. Appl. Math. Sci., 1, (2004).

405.      On the solution and applications of generalized equations using Newton's method, Applicationes Mathematicae, 31, 2, (2004), 229-242.

406.      A mesh independence principle for equations and their discretizations using Lipschitz and center Lipschitz conditions, Pan American Mathematical Journal, 14, 1 (2004), 69-82.

407.      A note on a new way of enlarging the convergence radius for Newton's method, Math. Sci. Res. J., 8, 5, (2004), 147-153.

408.      On two improved Durand-Kerner methods without derivatives, Communications on Applied Nonlinear Analysis, 11, 3, (2004), 43-48.

409.      A convergence analysis and applications for two-step methods in Banach space, Advances in Nonlinear Variational Inequalities, 7, 1 (2004), 59-78.

410.      An iterative method for computing zeros of operators satisfying autonomous differential equations, Southwest Journal of Pure and Applied Mathematics,1, (2004), 48-53, MR 2094206.

411.      On the comparison of a weak variant of the Newton-Kantorovich and Miranda theorems, J. Comput. Appl. Math., 166, 2, (2004), 585-589.

412.      A convergence analysis and applications for the Newton-Kantorovich method in K-normed spaces, Rendiconti del Circolo Mathematica di Palermo, LIII, (2004), 251-271.

413.      A convergence analysis for a certain class of quasi-Newton generalized Steffensen iterative methods, Advances in Nonlinear Variational Inequalities, 7, 1 (2004), 133-142.

414.      An improved convergence analysis for the secant method based on a certain type of recurrence relations, Intern. J. Comput. Math., 81, 5, (2004), 629-637.

415.      On a weak Newton-Kantorovich-type theorem for solving nonlinear equations in Banach space, Advances in Nonlinear Variational Inequalities, 7, 2 (2004), 101-109.

416.      On a Newton-Kantorovich-type theorem for solving equations in a Banach space and applications, Advances in Nonlinear Variational Inequalities, 7, 2 (2004), 79-88.

417.      Some convergence theorems for Newton's method involving center-Lipschitz conditions, Pan American Mathematical Journal, 14, 2, (2004), 75-84.

418.      On the convergence of Broyden’s method, Communications on Applied Nonlinear Analysis, 11, 4, (2004), 77-86.

419.      On the convergence of iterates to fixed points of analytic operators, Revue .Anal. Numer. Theor. Approx., 33, (2004), 11-17.

420.      Approximating solutions of equations using two-point methods, Appl. Num. Anal. Comp. Math.,1, 3, (2004), 386-412.

421.      New sufficient convergence conditions for the secant method, Chechoslovak Mathematical Journal, 55, 130, (2005), 175-187.

422.      A convergence analysis for Newton-like methods for singular equations using outer or generalized inverses, Applicationes Mathematicae, 32, 1, (2005), 37-49..

423.      A semilocal convergence analysis for the method of tangent parabolas, Rev. Anal. Numer. Theor. Approx., 34, 1, (2005), 3-15.

424.      On a two-point Newton-like method of convergence order two, Int. J. Computer Math., 88, 2, (2005), 219-234.

425.      Convergence radii for Newton’s method, Pan American Mathematical Journal, 15, 1, (2005), 12-28.

426.      Convergence radii for Newton’s method II, Pan American Mathematical Journal, 15, 1, (2005), 41-46.

427.      On the convergence of Newton’s method under twice-Frechet differentiability only at a point, Communications in Applied Nonlinear, 12, 1, (2005), 51-58.

428.      On the semilocal convergence of Newton’s method under weak Lipschitz continuous derivative, Advances in Nonlinear Variational Inequalities, 8, 1, (2005)71-82.

429.      On some theorems concerning the convergence of Newton methods, Advances in Nonlinear Variational Inequalities, 8, 1, (2005), 83-94.

430.      A semilocal convergence analysis for a deformed Newton method, Mathematical Sciences Research Journal, 9, 8, (2005), 217-222.

431.      On alternative directions to some theorems of Smale and Rheinboldt concerning Newton-like method, Advances in Nonlinear Variational Inequalities, 8, 1, (2005), 57-62.

432.      On a weak semilocal-local convergence theorem for Newton's method in Banach space, Advances in Nonlinear Variational Inequlaities, 8, 1, (2005), 103-110.

433.      On the semilocal convergence of the secant method under relaxed conditions, Advances in Nonlinear Variational Inequalities, 8, 1, (2005), 119-132.

434.      On the applicability of Newton's method for solving equations in a Banach space under center-Lipschitz-type conditions, Advances in Nonlinear Variational Inequalities, 8, 1, (2005), 1313-142.

435.      Concerning the convergence of a certain class of Newton-like methods in a Banach space, Advances in Nonlinear Variational Inequalities, 8, 1, (2005), 143-153.

436.      An improved approach of obtaining good starting points for solving equations by Newton's method, Advances in Nonlinear Variational Inequalities, 8, 1, (2005), 111-118.

437.      A semilocal convergence analysis of Newton's method involving operators with values in a cone, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 53-59.

438.      Ball convergence theorems for Newton’s method involving outer or generalized inverses, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 61-68.

439.      Lower and upper bounds for the distance of a manifold to a nearby point, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 69-73.

440.      On the weak Newton method for solving equations in a Banach space, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 49-52.

441.      Enlarging the radius of convergence for iterative methods by using a one parameter operator imbedding, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 75-80.

442.      On the Newton-Kantorovich method in Riemannian manifolds, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 81-85..

443.      On the computation of shadowing orbits for dynamical systems, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 87-91.

444.      On the semilocal convergence of the Gauss-Newton method, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 91-93.

445.      On the computation of continuation curves for solving nonlinear equations, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 101-108.

446.      Toward a unified convergence theory for Newton-like methods of “bounded deterioration”, Advances in Nonlinear Variational Inequalities, 8, 2, (2005), 109-120.

447.      Concerning the “terra incognita” between convergence regions of two Newton methods, Nonlinear Analysis, 62, (2005), 179-194.

448.      Enlarging the convergence domains of Newton’s method under regular smoothness conditions, Advances in Nonlinear variational Inequalities, 8, 2, (2005), 121-129.

449.      On a new iterative method of asymptotic order 1+√2 for the computation of  fixed points, Intern. J.Computer Mathematics, 82, 11, (2005), 1413-1428.

450.      On  an application of a weak Newton-Kantorovich theorem to nonlinear finite element analysis, Mathem. Sciences Research Journal, 9,12, (2005), 330-337.

451.      A unified approach for enlarging the radius of convergence for Newton’s method and applications, Nonlinear Functional Analysis and Applications, 10, 4, (2005), 555-563.

452.      On the approximation of solutions for generalized equations , Communications in Applied Nonlinear Analysis, 12,2,(2005),97-107.

453.      A new approach for finding weaker conditions for the convergence of Newton’s method, Applicationes Mathematicae, 32, 4, (2005), 465-475.

454.      A convergence analysis and applications of two-point Newton-Like methods in Banach space under relaxed conditions, Aequationes Mathematicae, 70, (2006), 124-148.

455.      On the solution of Variational Inequalities under weak Lipschitz conditions, Advances in Nonlinear Variational Inequalities, 9, 1, (2006), 85-94.

456.      A semilocal convergence analysis for Newton LP methods, Advances in Nonlinear Variational Inequalities, 9, 1, (2006), 75-84.

457.      A fine convergence analysis for inexact Newton methods, Functiones et Approximatio Commentari Mathematici, XXXVI, (2006),7-31.

458.      Relaxing the convergence conditions for Newton-like methods, J.Appl. Math. And Computing, 21, 1-2, (2006), 119-126.

459.      A weaker version of the shadowing lemma for operators with chaotic behavior, ,Intern. J. Pure and Appl. Math., 28, 3, (2006), 417-422.

460.      A convergence analysis of a Newton-like method without inverses., Int. J. Pure and Appl. Math., 30, 2, (2006), 143-149.

461.      On the convergence of Newton’s method using the inverse function theorem, Nonlinear Funct. Anal. And Appl.,11, 2, (2006), 201-214.

462.      On the secant method for solving non-smooth equations, J. Math. Anal. Appl., 322, 1, (2006), 146-157, MR2238155 65H10, (47125,90C56).

463.      On the convergence of fixed slope iteartions, PUJM, 38, (2006), 39-44.

464.      Local convergence of the curve tracing for the homotopy method, Revista Colombiana des Matematicas, 40, (2006), 417-422.

465.      Quasi-Newton methods for solving generalized equations, Nonlinear Functional Analysis and Applications, 11, 4, (2006), 647-654.

466.      Local convergence of Newton’s method for perturbed generalized equations, J. Korean Soc. Math. Educ. Ser. B. Pure and Applied Math., 13,4, (2006), 261-267.

467.      On an improved unified convergence analysis for a certain class of Euler-Halley-type methods, J. Korean Soc. Math. Educ.Ser.B.,13,3, (2006), 207-216.

468.      An improved convergence analysis of a super quadratic method for solving equations, Revista Colombiana des Matematicas, 40,1,(2006),65-73.

469.      A refined Newton’s mesh independence principle for a class of optimal shape design problems, Central European J. Math., 4, 4, (2006), 562-572.

470.      A weaker affine covariant Newton-Mysovskikh theorem for solving equations, Applicationes Mathematicae, 33,3-4, (2006), 355-363.

471.      Convergence of Newton’s method under the gamma condition, Proyecciones,Iniversidad Catolica De Norte, 25, 3, (2006), 293-306.

472.      Local convergence of Newton’s method under a weak gamma condition, Punjab University Journal of Mathematics (PUJM), 38, (2006), 1-7.

473.      A unifying local and semilocal convergence analysis of Newton-like methods, Advances in Nonlinear Variational Inequlities, 10,1,(2007),1-12.

474.      On the solution of variational inequalities on finite dimensional spaces, Advances in Nonlinear Variational Inequalities,10,(1,(2007),69-77.

475.      Local convergence of Newton’s method for generalized equations under Lipshitz conditions on the Frechet derivative, Advances in Nonlinear Variational Inequalities, 10, 1, (2007), 101-111.

476.      On the convergence of Newton’s method for a class of non-smooth operators, J. Comput. Appl. Math., 205, (2007), 584-593.

477.      A Kantorovich-type analysis for a fast iterative method for solving nonlinear equations, J.  Mathem. Anal. Applic., 332, (2007), 97-108.

478.      On the convergence of the Secant method under the gamma condition, Central European Journal of mathematics, 5, 2, (2007), 205-214.

479.      On the solution of nonlinear complementarity problems, Advances in Nonlinear Variational Inequalities, 10, 1, (2007), 79-88.

480.      On the convergence of the structured PSB update in Hilbert space, International Journal of Pure and Applied Mathematics, 34, 4, (2007), 519-524.

481.      A non-smooth version of Newton’s method using Locally Lipschitzian operators, Rendiconti Circolo Matematico Di Palermo, 56, (2007),  Ser.II,Tomo, LVI, (2007), 5-16.

482.      On a fast two-step method for solving nonlinear equations, International Journal of Pure and Applied Mathematics, 34, 3, (2007), 313-321.

483.      An improved convergence and complexity analysis of Newton’s method for solving equations, International Journal of Computer  Mathematics, 84, 1, (2007), 67-73.  

484.      A non-smooth version of Newton’s method based on Holderian assumptions, International Journal of Computer Mathematics, 84, 12, (2007), 1747-1756.

485.      On the solution of variational inequalities on finite dimensional spaces, Advances in Nonlinear Variational Inequalities, 10, 1, (2007), 69-77.

486.      On  the convergence of Broyden-like methods, Acta Mathematica Sinica,English Series, 23, 6, (2007), 965-972

487.      Weaker conditions for the convergence of Newton-line methods, Revue D’Analyse Numer. Theor. Approx., 36, 1, (2007), 39-49.

488.      An extension of the contraction mapping principle, J. Korean Soc. Math. Ed.Ser. B.Pure and Appl. Math.,14,4,(2007),283-287.

489.      On the local convergence of Newton’s method on Lie Groups, Pan American Math.,  J.17,4,(2007),101-109.

490.      A note on the solution of a nonlinear singular equation with a shift in a generalized Banach space, Journal Korea. S. M. E. Ser. B., 14, 4, (2007), 279-282.

491.      An improved unifying convergence analysis of Newton’s method on Riemannian manifolds, J. Appl. Math. And Computing, 25, 1-2,  (2007),

492.      On the gap between the semilocal convergence domain of two Newton methods, Applicationes Mathematicae, 34, 2, (2007), 193-204.

493.      On a quadratically convergent iterative method using divided differences of order one, J. Korea S. M. E. Ser. B., 14, 3, (2007), 203-221.

494.      An improved local convergence analysis for secant-like methods, East Asian Math. J., 23, 2, (2007), 261-270.

495.      Approximating solutions of equations using Newton’s method with a modified Newton’s iterate as a starting point. Revue D’Analyse Numer. et de Th. Approx., 36, 2, (2007), 123-137.

496.      An improved convergence analysis for the secant method under the gamma condition, PUJM, 39, (2007), 1-11.

497.      Newton’s method for variational inclusions under conditioned Frechet derivative, Applicationes Mathematicae, 34, 3, (2007), 349-357.

498.      On the convergence of the Newton-Kantorovich method:The generalized Holder case. Nonlinear studies, 14, 4, (2007), 355-364.

499.      A refined theorem concering the conditioning of semidefinite programs, J. Appl. Math. and Computing., 24(1-2), (2007), 305-312.

500.      A cubically convergent method for solving generalized equations without second order derivatives, Intern J. Modern Math, 3, 2, (2008), 187-196.

501.      Solving equations using Newton’s method on a Banach space with a convergence structure.  Revue D’Anal. Numer. Th. Approx., 37, 1, (2008), 17-26.

502.      Concerning the convergence of Newton’s method under Vertgeim-type conditions, Nonlinear Functional Analysis and Application, 13, 1, (2008), 43-59.

503.      A finer mesh independence of Newton’s method, Nonlinear Functional Analysis and Application, 13, 3, (2008), 357-365.

504.      A semilocal convergence analysis for a certain class of modified Newton processes, East Asian J. Math., 24, 2, (2008), 151-160.

505.      Improved convergence results for generalized equations, East Asian Math. J., 24, 2, (2008), 161-168.

506.      A Kantorovich analysis of Newton’s method on Lie groups, J. Concrete and Applicable Anal., 6, 1, (2008), 21-32.

507.      Local convergence of inexact Newton methods under general conditions, Intern J. Modern Mathem., 3, 1, (2008), 11-19.

508.      A weak Kantorovich existence theorem for the solution of nonlinear equations, J. Math. Anal. Appl., 342, (2008), 909-914.

509.      On the Secant method for solving nosmooth equations and nondiscrete induction, Nonlinear Functional  Analysis and Applications, 13, 1, (2008), 147-158.

510.      Steffensen methods for solving generalized equations, Serdica Mathem. J., 34, (2008), 1001-1012.

511.      On a secant –like method for solving generalized equations, Mathematica Bohemica, 133, 3, (2008), 313-320.

512.      On the convergence of the midpoint method, Numerical Algorithms, 47, (2008), 157-167.

513.      On the semilocal convergence of a Newton-type method in Banach spaces under the gamma-condition, J. Concrete and Appl. Anal., 6, 1, (2008), 33-44.

514.      On the convergence of Newton’s method and locally Holderian operators, J. Korea Math. Soc. Math. Educ. Ser. B: Pura and Appl. Math., 15, 2, (2008), 111-120.

515.      Local convergence for multistep simplified Newton-like methods, PUJM, 40, (2008), 1-7.

516.      On a two step Newton method for solving equations under inproved Ptak-type estimates, Commun. on Applied Nonlin. Anal., 15, 1, (2008), 85-93.

517.      On the radius of convergence of Newton’s method under average mild differentiability conditions. Nonlinear Functional Analysis and Applications, 13, 3, (2008), 409-415.

518.      On the semilocal convergence of a fast two step method, Revista Colombiana de Matematicas, 42, 1, (2008), 1-10.

519.      Approximating solutions of equations by combining Newton like methods. J. Korea Math. Soc. Educ. Ser. B: Pure and Appl.Math., 15, 1, (2008), 35-45.

520.      Concerning the radii of convergence for a certain class of Newton-like methods. J. Korea Math. Soc. Educ. Ser. B: Pure and Appl.Math., 15, 1, (2008), 47-55.

521.      Local convergence of the secant method under Holder continuous divided differences, East Asian J. Math., 24, 1, (2008), 21-26.

522.      On the local convergence of a two step Steffensen-type method for solving generalized equations, Proyecciones,  27, 3, (2008), 319-330.

523.      On the local convergence of a Newton-type method in Banach space under the gamma condition, Proyecciones, 27, 1, (2008), 1-14.

524.      An inverse free Newton-Jarratt-type iterative method for solving equations, J. Appl. Math. Computing, 1-2, 28, (2008), 15-28.

525.      A comparative study between convergence theorems for Newton’s method, J. Korea Math. Soc. Educ. Ser. B: Pure and Appl. Math., 15, 4, (2008), 365-375.

526.      Concerning the semilocal convergence of Newton’s method under convex majorants, Rendiconti Circolo Matematico di Palermo, 57, (2008), 331-341.

527.      On a quadratically convergent method using divided differences of order one under the gamma condition, Central European J. Math., 6, 2, (2008), 262-271.

528.      On the midpoint method for solving generalized equations, PUJM, 40, (2008), 63-70.

529.      On the Newton –Kantorovich and Miranda theorems, East Asian J. Math., 24, 3, (2008), 289-293.

530.      On the semilocal convergence of Newton-like methods for solving equations containing a nondifferentiable term, East Asian J.Math., 24, 3, (2008), 295-304.

531.      Multipoint method for generalized equations under mild differentiability conditions,Functiones et Approximation, Comentarii Matematici, 38, 1, (2008), 7-19.

532.      Newton’s method in Riemannian manifolds, Revue D’Analyse Numérique et de Théorie D’ Approximation, 37, 2, 1, (2008), 119-125.

533.      A refined semilocal convergence analysis of an algorithms for solving the Ricatti equation, J. Appl. Math. Computing., 27(1-2), (2008), 339-344.

534.      A Fréchet –derivative free cubically convergence method for set valued maps, Numerical Algorithms, 4, 48, (2008), 361-371.

535.      A cubically convergent method for solving generalized equations. Inter. J. Modern Math., 3(2), (2008), 187-195.

536.      Local convergence analysis for a certain class of inexact methods, The Journal of Nonlinear Sciences and its Applications, 2, 1, (2009), 11-18.

537.      On the comparison of a Kantorovich-type and Moore Theorems, J. Appl. Math. and Computing, 29, (2009), 117-123.

538.      Concerning the convergence of Newton’s method and quadratic majorants, J. Appl. Math. and Computing, 29, (2009), 391-400.

539.      Newton’s method for approximating zeros of vector fields on Riemannian manifolds, J. Appl. Math. and Computing, 29, (2009), 417-427.

540.      On the convergence of inexact Newton-type methods using recurrent functions, Pan American Math. J., 19, 1, (2009), 79-96.

541.      Local convergence of inexact Newton-like methods, The Journal of Nonlinear Sciences and its Applications, 2(1), (2009), 11--18.

542.      Local convergence results for Newton’s method, J. Korea Math. Soc. Educ. Ser. B: Pure and Appl. Math., 16, 1, (2009).

543.      An improved Newton-Kantorovich theorem and interior point methods, East Asian J. Math., 25, 2, (2009), 147-151.

544.      Convergence of the Newton method for Aubin continuous maps, East Asian J. Math., 25, 2, (2009), 153-157.

545.      Local convergence of Newton-like methods for generalized equations, East Asian J. Math., 25, 4, (2009), 425-431.

546.      On the semilocal convergence of inexact Newton methods in Banach spaces, J. Comput. Appl. Math., 228, 1, (2009), 434-443.

547.      A convergence analysis of Newton’s method under the gamma condition in Banach spaces, Applicationes Mathematicae, 36, 2, (2009), 225-239.

548.      On Ulm’s method for Frechet differentiable operators, J. Appl. Math. Computing, 31,(1-2), (2009),97-111.

549.      On Ulm’s method using divided differences of order one, Numerical Algorithms, 52, (2009), 295-320.

550.      On a class of Newton-like methods for solving nonlinear equations, J. Comput. Appl. Math., 228, (2009), 115-122.

551.      A generalized Kantorovich theorem on the solvability of nonlinear equations, Aequationes Mathematicae, 77, (2009), 99-105.

552.      An improved mesh independence principle for solving equations and their discretizations using Newton’s method, Australian J. Mathematical Analysis and Applications, 6, 2, 2, (2009), 1-11.

553.      Finding good starting points for solving equations by Newton’s method, Revue D’Analyse Numerique et de Theorie de l’Approximation, 39, 1, (2010), 3-10.

554.      On the Newton Kantorovich theorem and nonlinear finite element methods, Applicationes Mathematicae, 36, 1, (2009), 75-81.

555.      Newton’s method on Lie Groups, J. Appl. Math. Computing, 31,(1-2), (2009), 217-228.

556.      On local convergence of a Newton-type method in Banach spaces, Intern. J. Computer Math., 86(8), (2009), 1366-1374.

557.      On an improved local convergence analysis for the Secant method, Numerical Algorithms, 52, (2009), 257-271.

558.      Semilocal convergence of Newton’s method under a weak gamma condition, ANVI, 13, 1, (2009), 65-73.

559.      Convergence analysis for Steffensen-Like method, Nonlinear Functional Analysis and Applications, 1, (2010), 21-32, Nova science Publ.Inc.

560.      On the local convergence of the midpoint method in Banach spaces under the gamma- condition, Proyecciones J. Math., 28, 2, (2009), 155-167.

561.      On the convergence of a modified Newton method for solving equations, PUJM, 41, (2009), 11-21.

562.      On the convergence of Steffensen’s method on Banach spaces under the gamma-condition, Communications on Applied Nonlinear Analysis, 16, 4, (2009), 73-84.

563.      A new semilocal convergence theorem for Newton’s method under a gamma-type condition. Atti Semin. Fis. Univ. Modena Reggio Emilia, 56, (2008-2009), 31-40.

564.      An improved local convergence analysis for a two-step-Steffensen-type method, J. Appl. Math. Computing, 30, (2009), 237-245.

565.      Generalized equation, variational inequalities and a weak Kantorovich theorem, Numer. Alg., 52, (2009), 321-333.

566.      Convergence theorems for Newton’s method and modified Newton’s method, J. Kor. Soc. Math. Ser. B. Pure and Applied Math., 16, 4, (2009).

567.      An improved convergence analysis of Newton’s method for systems of equations with constant rank derivatives, Mathematica, 51, 74, 2, (2009), 1-14.

568.      On the convergence of the modified Newton’s method under Holder continuous Fréchet-derivative,  Appl. Math. Comput., 213, (2009), 440-448.

569.      On the convergence of modified Newton methods for solving equations containing a nondifferentiable, term, J. Comput. Appl. Math., 231(2), (2009), 897-906.

570.      On the convergence of a Jarratt-type method using recurrent functions. J. Pure and Appl. Math.: Advances and Applications, 2(2), (2009), 121-144.

571.      On multipoint iterative processes of efficiency index higher than Newton’s method, J. Nonlinear science Appl., 2, (2009), 195-203.

572.      On the implicit iterative processes for strictly pseudocontractive mappings in Banach spaces, J. Comput. Appl. Math., 233, 2,(2009), 208-216.

573.      Enclosing roots of polynomial equations and their applications to iterative processes, Surveys in Mathematics and its Applications, 4, (2009), 119-132.

574.      On the convergence of Newton-type methods under mild differentiability conditions, Numerical Algorithms, 52, 4, (2009), 701-726.

575.      On the convergence of some iterative procedures under regular smoothness, Pan. Amer. Math. J., 19, 2, (2009), 17-34.

576.      On the convergence of two step Newton-type methods of high efficiency index, Applicationes Mathematicae, 36, 4, (2009), 465-499.

577.      On the convergence of  Stirling’s method in Banach spaces under gamma-type condition, ANVI, 12, 2, (2009), 17-23.

578.      On the convergence of Newton’s method and locally Holderian inverses of operators, J. Korean Soc. Math. Educ. Ser. B Pure and Applied math., 16, 1, (2009), 13-18.

579.      On the local convergence of the Gauss-Newton method, PUJM, 41, (2009), 23-33.

580.      An improved local convergence analysis for Newton-Steffensen-type methods, J. Appl. Math. and Computing, 32, (2010), 111-118.

581.      Inexact Newton methods and an improved conjugate gradient solver for normal equations, Nonlinear Functions  Analysis and Applications., 2, (2010), 155-166.

582.      An improved convergence and complexity for the interpolatory Newton method, Cubo Math. Journal, 12, 1, (2010), 151-161.

583.      On the convergence of Stirling’s-type  methods using recurrent functions, PanAmerican  Math. J., 20, 1, (2010), 93-105.

584.      On the feasibility of continuation methods form solving equations, ANVI, 13, 1, (2010), 57-63.

585.      Improved estimates on majorizing sequences for the Newton-Kantorovich method, J. Appl. Math. and Computing, 32, (2010), 1-18.

586.      On the semilocal convergence of a Newton-type method of order three, J. Korea S. M. A. Ser. B.Pure and Appl. Math., 17, 1, (2010), 1-27.

587.      A convergence analysis of Newton-like method for singular equations using recurrent functions, Numerical Functional Analysis and Optimization, Issue31, 2, (2010),112-130.

588.      Convergence conditions for the secant method, Cubo Math. Journal, 12, 1, (2010), 163-176.

589.      A Kantorovich-type analysis of Broyden’s method using recurrent functions, J. Appl. Math. Computing,32,2,(2010),353-

590.      A generalized  Kantorovich theorem for nonlinear equations based on function splitting, Rend. Circ. Matem. Palerm.2,58,3,(2009),441-451.

591.      A new semilocal convergence Analysis for a fast iterative method for nondifferentiable operators, J. Appl. Math. and Computing., DOI:10.1007/s12190-009-0303-0.

592.      On Newton’s method for solving equations containing  Frechet differentiable operators of order at least two, J. Appl. Math. Comput., DOI:/j.amc.2009.07.005.

593.      On a class of secant-like methods for solving equations, Numer. Alg.,54,(2010),485-501.

594.      On the  Gauss-Newton method, J. Appl. Math. Comput.,35,1,(2011),537-.

595.      On the convergence of Newton’s method under mild differentiability conditions,using recurrent functions, J. Complexity, DOI:10.1016/J.Co.2009.06.003.

596.      A Kantorovich-type convergence analysis  of The Newton-Josephy method for solving variational inequalities ,Numer. Algorithms, 55,(2010),447-466.

597.      Tabatabaistic regression and its applications to the space shuttle challenger O-ring data, J. Appl. Math. and Computing,33,(2010),513-523.

598.      A Convergence analysis for  directional two step Newton methods, Numerical Algorithms, 55,(2010),503-528.

599.      Improved generalized differentiability conditions for Newton-like methods, J. Complexity,26,(2010),316-333.

600.      A Newton-like method for nonsmooth variational inequalities, Nonlinear Analysis: T.M.A., DOI:10.1016/j.na.2010.01.022.

601.      Improved results on estimating and extending the radius of the attraction ball, Appl. Math. Letters,23,(2010),404-408.

602.      On Newton like methods of “bounded deterioration” using recurrent functions, Aequationes Mathematicae.,79,(2010),61-82.

603.      On the solution of nonlinear equations containing a nondifferentiable term, East Asian J. Math., accepted.

604.      Newton’s method and interior point techniques, Pan Amer.Math.J.20,4,(2010),93-100.

605.      An improved convergence analysis for the Newton Kantorovich method under recurrence relations, Intern J. Computer Math., accepted.

606.      Hummel-Seebeck method for generalized equations under conditioned second Fréchet –derivative, Nonlinear Functional Analysis and Applications, accepted.

607.      Extending the application of the shadowing lemma for operators with chaotic behavior,East Asian Math.J.27,5,(2011),521-525.

608.      On the convergence region of Newton’s method under Holder continuity conditions, Intern. J. Computer Mathematics, accepted.

609.      Newton-like method for nonsmooth subanalytic variational inequalities, Mathematica,52,75,1,(2010),5-13.

610.      A semilocal convergence analysis for directional Newton methods, Mathematics of Computation, Amer. Math. Soc.,80,273,(2011),327-343.

611.      Convergence conditions for secant-type methods, Chehoslovak J.Math.,60,135,(2010),253-272.

612.      On the convergence of Newton-type methods using recurrent functions, Intern .J. Computer Math.,87,14,(2010),3273-3296.

613.      On Newton’s method using recurrent functions and hypotheses on the first and second Frechet-derivatives, Atti del Seminario Matematico e Fisico Dell”Universita di Modena.,Regio Emilia,57,(2010),1-18.

614.      On the semilocal convergence of Newton-like methods using recurrent polynomials, Revue D’Analyse Numérique et de la Théorie de l’Aprroximation, accepted.

615.      On Newton’s method for solving equations and function splitting, Numerical Mathematics: Theory methods and applications,4,1,(2011),53-67.

616.      On Newton’s method defined on not necessarily  bounded domains, J. Pure and Appl. Math.: Advances and Applications,3,1,(2010),1-16.

617.      Secant-like method for solving generalized equations, Methods and Applications of Analysis,16,4,(2009),469-478.

(J3) Submitted for Publication /Under Preparation

618.      On the semilocal convergence of Newton’s method under unifying conditions.

619.      On the convergence of Newton-like methods under general and unifying conditions.

620.      On  the monotone convergence of an iterative method without derivatives.

621.      On a unifying convergence analysis of two-step two-point Newton methods for solving nonlinear equations.

622.      On the solution of generalized equations under Holder continuity conditions

623.      A fast Dontchev-type iterative method for solving generalized equations.

624.      On the solution of nonsmooth generalized equations.

625.      On the convergence of Newton’s method for set valued maps under weak conditions.

626.      An improved convergence analysis of one step intermediate Newton iterative scheme for nonlinear equationsJ. Appl.Math.Computing,38,(2012),243-256.

627.      A generalized Kantorovich theorem on the solvability of nonlinear equation,Aequationes Mathematicae,77,1-2,(2009),99-105.

628.      An intermediate Newton iterative scheme and generalized Zabrejko-Nguen and Kantorovich existence theorems for nonlinear equations.

629.      Newton-like methods with at least quadratic order of convergence for the computation of fixed points,PUJM,43,(2011),8-18.

630.      Majorizing functions and two point Newton methods,J.Comput.Appl.Math.234,(2010),1473-1484.

631.      Superquadratic method for generalized equations under relaxed condition on the second Fréchet derivative.

632.      Local convergence of Newton’s method using Kantorovich majorants,Revue D’Analyse Numer.De Th.Approx.2,(2010),97-106.

633.      On the semilocal convergence of Ulm’s method.

634.      An improved local convergence analysis for secant –like method.

635.      On the semilocal convergence of the secant method with regularly continuous divided differences.

636.      Newton’s method and regularly smooth operator, Revue D’Analyse Numeriq.De Th.Approx.2,(2010)

637.      On the semilocal convergence of Newton-like methods using decreasing majorizing sequences.

638.      On the semilocal convergence of Stirling’s method using noncontractive  hypotheses.

639.      On the semilocal convergence of Steffensen’s method using decreasing majorizing sequences.

640.      On a theorem from interval analysis for solving nonlinear equations,Australian J. Math. Anal.Applic..

641.      On Newton’s method for solving equations containing nosmooth operators.

642.      On the Secant method for solving equations containing nosmooth operators.

643.      Newton’s method on Riemannian manifolds.

644.      On the conditioning of semidefinite programs.

645.      Newton’s method for solving a class of optimal design problems.

646.      Traub-Potra type method for set-valued maps,Austral.J.Math.Anal.Applic.

647.      On a generalization of Moret’s theorem for inexact Newton-like methods,Pan Amer. Math. J.22,1,(2012),67-73.

648.      On an improved local convergence analysis for the secant method.

649.      On the Gausss-Newton method for solving equation,Proyecciones J. Math.31,1,(2012),11-24.

650.      Newton-Steffensen type method for perturbed nonsmooth subanalytic variational inequalities.

651.      Extending the Newton-Kantorovich hypothesis for solving equations,J.Comput.Appl.math.234,10,(2010),2993-3006.

652.      A Kantorovich-type analysis of Broyden’s method using recurrent function,J.Appl.Math.Computing,32,2,(2010),353-.

653.      On the semilocal convergence of Werner’s method  for solving equations using recurrent function,PUJM,43,(2011),19-28.

654.      On the convergence of Steffensen-type method using recurrent functions,Revue D’Analyse Numerique et De Th.Approx.38,2,(2009),130-143.

655.      Inexact Newton-type methods,J.Complexity(2010).

656.      On the local convergence analysis of inexact Gauss-Newton-like methods,Pan American J.Math.21,3,(2011),11-18.

657.      On the convergence of Newton-like methods for solving equations using slantly differentiable operators.

658.      On the solution of generalized equations and variational inequalities,Cubo,13,1,(2011),39-54.

659.      On the midpoint method for solving equations,Apl.Math.Comput.216,8,(2010),2321-2332.

660.      On the semilocal convergence of the Halley method using recurrent functions,J.Appl.Math.Computing,37,1,(2011),221-246.

661.      On the semilocal convergence of Newton’s method, when  the derivative is not continuously invertible,Cubo,13,1,(2011),39-54.

662.      A note on the improvement of the error bounds for a certain class of operators.

663.      Locating roots for a certain class of polynomial,East Asian math.J.26,1,(2010),351-363.

664.      Weak sufficient convergence conditions for some accelerated successive approximations.

665.      Extending the applicability of a Secant type method of order two using recurrent functions.

666.      Local results for a continuous analog  of Newton’s method,East Asian Math. J.3,26,(2010),365-370.

667.      Improved results for continuous modified Newton-type methods,Mathematica,53,76,1,(2011),1-14.

668.      A derivative free quadratically convergent iterative method for solving least squares problems,NUMA,58,(2011),555-571.

669.      Kantorovich –type semilocal convergence analysis for inexact Newton methods,J.Comput.Appl.math.235,11,(2011),2993-3005.

670.      On the convergence of a derivative free method using recurrent function,J.Appl.Math.Computing.

671.      On an iterative method of Ulm-type for solving equations.

672.      On the convergence of inexact Newton-type methods under weak conditions.

673.      Directional secant type method for solving equations.

674.      A convergence analysis for directional Newton-like methods,Communications on Applied Nonlinear Anal.18,4,(2011),24-38.

675.      A comparison between two techniques for directional cubically convergence Newton methods,NFAA.

676.      Directional Chebyshev –type methods for solving equations.

677.      On the semilocal convergence of efficient Chebyshev-secant-type methods,J.Comput.Appl.Math.235,10,(2011),3195-3206.

678.      On the semilocal convergence of Steffensen’s method<Mathematica 53,76,2,(2011),1-13.

679.      A unified approach for the convergence of a certain numerical algorithm using recurrent functions,Computing,90,3,(2010),131-164.

680.      Semilocal convergence conditions for the secant method using recurrent functions.

681.      Newton-Steffensen methods for solving generalized equations,Pan Amer.Math.J.21,2,(2011),45-57.

682.      Convergence of directional Newton methods undermild differentiability and applications,Applied Mathematics andComputation217,(2011),8731-8746.

683.      Local convergence of a Secant –type method for solving least square problems,Appl.Math.Comput.217,(2010),3816-3824.

684.      Local convergence of a three point method for solving least square problems,Numerical Functional Analysis and Applications,15,(2010),3816-3824.

685.      On Newton’s method using recurrent functions under hypotheses up to the second Frechet derivative,J.K.S.ME.

686.      Convergence domains under Zabrejko-Zincenko conditions for  Newton-type methods using recurrent functions,Appl.Math.38,2,(2011),193-209.

687.      On the solution of systems of equations with constant rank derivatives,Numer. Algor.

688.      Semilocal convergence of Newton’s method for singular systems with constant rank derivatives,J.Korean Soc.Math.Ed.Ser.B.Pure and Appl.Math.18,2,(2011),.

689.       Newton-type  methods,Advances in Nonlinear Variational Inequalities,14,2,(2011),65-79.

690.      Newton Kantorovich approximations under weak continuity condition,J.Appl.Math. Computing,37,1,(2011),361-375.

691.      Newton-type method in K-normed spaces,Numer. Funct.Anal. Applic.

692.      On the semilocal convergence of the Gauss-Newton method using recurrent functions,J.KSME,Ser.B.17,4,(2010),307-319.

693.      A unifying theorem for  Newton’s method on spaces with a convergence structure,J.Complexity,(2010).

694.      Convergence radius of the modified Newton method for multiple zeros under Holder continuous derivative,Appl.Math.Comput.2,217,(2010),612-621.

695.      Sixth order derivative free family of iterative method,Appl.math.Comput..

696.      A relationship between Lipschitz constants appearing in Taylor’s formula,J.Korean math. Soc.math. Educ.Ser.B.Pure and Applied math.18,4,(2011),345-351.

697.      On the convergence of Newton’s method under w^*-conditioned second derivative,Appl.Math.38,3,(2011),341-355.

698.      Approximation methods for common solutions of generalized equilibrium problems of nonlinear

699.      Variational inequalities problems and fixed point problems,computers and mathematics with applications 60,(2010),2292-2301.

700.      On the quadratic convergence of Newton’s method under center-Lipschitz but not necessarily Lipschitz hypotheses.

701.      On the convergence of Newton-like methods using outer inverses but no Lipschitz condition,Nonlin.Funct.Anal.Applic.

702.      A note on the iterative regularized Gauss-Newton method under center-Lipschitz conditions,Commun.Appl.Non.Anal.18,4,(20011),89-96.

703.      A note on a method for solving inverse problems.

704.      On the convergence of inexact two-step Newton-type methods  using recurrent functions,East Asian J. math.27,3,(2011),319-338.

705.      On the convergence of inexact two-step Newton-like algorithms using recurrent functions,J.Appl.Math. Computing,38,1,(2012),,41-61.

706.      A new convergence analysis for the two step Newton method of order three.

707.      A new convergence analysis for the two step Newton method of order four.

708.      Inexact Newton methods and recurrent functions,Appl.Math.37,1,(2010),113-126.

709.      A new semilocal convergence analysis for the Jarratt method.

710.      Extending the applicability of the Gauss Newton method under average Lipschitz –type conditions,Numer. Algor.,DOI:10.1007/s11075-011-9466-9.

711.      On the semilocal convergence of Newton’s method using majorants and recurrent functions,Numer.Funct.Anal.Applic.

712.      Chebyshev-Secant –type methods for nondifferentiable operators

713.      Note on quadrature based two step iterative methods for nonlinear equations.

714.      On the radius of convergence of some Newton-type methods in Banach spaces,J.Korean Math. Soc.Ser. B.18,3,(2011),

715.      On the semilocal convergence of an inverse free Broyden’s method,PanAmer. Math.J.20,4,(2010),77-92.

716.      Extended sufficient semilocal convergence conditions for the secant method,Computers and Math.with Appl. 62,(2011),599-610.

717.      On the convergence of Broyden’s method in Hilbert space.

718.      On the Halley method,Applic. Math.

719.      Improved local analysis for a certain class of iterative methods with cubic convergence,Numa.

720.      Optimal Newton-type methods for solving nonlinear equations,Advanc. Non.Variat. Ineq.14,1,(2011),47-59.

721.      Ball convergence theorems for Halley’s method in Banach spaces.J.Appl.math.Comput. 38,1,(2012),453-465.

722.      Improved ball convergence of Newton’s method under general conditions,Appl.Math.

723.      On the semilocal convergence of derivative free methods for solving equations.

724.      A simplified proof of the Kantorovich theorem for solving equations using scalar telescopic series and related weaker extensions.

725.      A survey on extended convergence domains for the Newton Kantorovich method.

726.      Chebyshev-Kurchatov-type methods for solving equations with non-diffeentiable operators.

727.      On the semilocal convergence of a derivative free Chebyshev-Kurchatov three step method for solving equations.

728.       Weak convergence conditions for Newton-like methods

729.      Weaker w-convergence conditions for the Newton-Kantorovich method.

730.      An intermediate Newton-Kantorovich method for solving nonlinear equations

731.      Unified majorizing sequences for Traub-type multipoint iterative procedures.

732.      New convergence conditions for the secant method.

733.      Majorizing sequences for iterative methods.J.Comput.Appl.Math.(2011).

734.      On the method of chord for solving nonlinear equations.

735.      Majorizing sequences of arbitrary high convergence order for iterative procedures.

736.      Improved local convergence of Newton’s method under weak majorant condition,J.Comput. Appl.Math. 236,(2012),1892-1902.

737.      Extending the applicability of the mesh independence principle for solving nonlinear equations.

738.      On the convergence of a Newton-like method under weak conditions.Commun.Koren Math.Soc.26,4,(2011),575-584.

739.      On the computation of fixed points for random operator equations.

740.      Weak convergence conditions for Newton’s method in Banach space using general majorizing sequences.

741.      Extending the applicability of the secant method and nondiscrete induction,Appl.math.Comput. 218,(2011),3238-3246.

742.      Extending the applicability of Newton’s method and nondiscrete induction,Applied Mathematics and Computation,(2011)26-40.

743.      Weaker conditions for the semilocal convergence of Newton’s method,J.Complexity.

744.      Extending the applicability of Newton’s method under Holder differentiability conditions.

745.      Secant-type methods and nondiscrete induction.

746.      On the convergence of a double step Secant method and nondiscrete induction.

747.      How to develop fourth and seventh order iterative methods.Novidad  Sad J. Math,40,2,(2010),61-67.

748.      On the convergence of Broyden-like methods using recurrent functions,Numer.Funct. Anal.Optimiz.32,1,(2011),26-40.

749.      On the local convergence of inexact Newton-like methods under residual control-type conditions,J.Comput.Appl.math.235,(2010),218-228.

750.      Weak convergence conditions for inexact Newton-type methods,Applied Mathematics and computation,218,(2011),2800-2809.

751.      Extending the applicability of Newton’s method on Lie groups.

752.      On the semilocal convergence of a damped Newton’s method

753.      On the convergence of Newton’s method under uniformly continuity conditions

754.      A unifying convergence analysis for Newton’s method and twice Frechet differentiable operators.

755.      Efficient three step Newton-like methods for solving equations

756.      Convergence of a Gauss Newton method for convex composite optimization.

757.      Local convergence analysis of proximal Newton-Gauss method

758.      A finer discretization aand mesh independence of Newton’s method for solving generalized equations.

759.      New conditions for the convergence of Newton-like methods and applications

760.      Estimating upper bounds on the limit points of majorizing sequences for Newton’s method

761.      Weaker convergence conditions for the secant method.

762.      Weaker conditions for Newton’s method under mild differentiability.

763.      The majorant method in the theory of Newton-Kantorovich approximations and generalized Lipschitz conditions

764.      Extending the applicability of two point Newton-like methods under generalized conditions

765.      Majorizing sequences for Newton’s method under centered conditions for the derivative.

766.      Expanding the applicability of high order-Traub-type procedures and their applications

767.      Local convergence of efficient secant-type methods for solving nonlinear equations,Applied Mathematics and computation.

768.      Efficient Steffensen-type algorithms for solving nonlinear equations

769.      An extension of Argyros’ Kantorovich-type solvability theorem for nonlinear equations,PAnAmer. Math.J. 22,1,(2012),57-66.

(K) REPRINT(S) REQUESTS

The following professors have requested papers:

1. Etzio Venturino, University of Iowa, (Dept. Math.), USA

2. C.G. Lopez, Madeira, Portugal

3. H. Jarchow, Institute fur Angewandte Mathematik der Universitat Zurich Ch-8001 Zurich, Switzerland.

4. M.S. Khan, King Abdulaziz University, (Dept. Math.), Saudi Arabia

5. Manfred Knebusch, Universitat Regensburg Fakultat fur Mathematik 8400 Regensburg Universitatsstrabe 31, West Germany

6. Ernest J. Eckert, College of Environmental Sciences, The University of Wisconsin-Green Bay, 2420 Nicolet Dr., Green Bay, WI 54302, USA

7. Josef Danes, Mathematical Institute Charles University, Sokolovska 83 18600 Prague 8-Karlin, Chechoslovakia

8. Goral Reddy, Dept. of Mathematics, St. Andrews, Scotland

9. Jerzy Popenda, Dept. of Math., Univesity of Poznan, Poland

10. Vlastimil Ptak, Chechoslovak Academy of Science, Praha, Chechoslovakia

11. Alejandro Figueroa, Universidad de Magallanes, Punta Arenas-Chile

12. Dragan Jucic, Osijek, Yugoslavia

13. Ahmad B. Casdam, Multan, Pakistan

14. Luis Saste Habana, Cuba

15. S.N. Mishra, Lesotho, Africa

16. Josef Kral, Prague, Checholovakia

17. Juan J. Nieto, Santiago, Spain

18. S.D. Chatterji, Lausanne, Switzerland

19. Peter Madhe, Berlin, Germany

20. Ioan Muntean, Cluj, Romania

21. S.L. Singh, Xardwar, India

22. P.D.N. Sriniras, India

23. S. Grzegorskii, Lublin, Poland

24. Toma's Arechaga, Aires, Argentina

25. J.D. Deader, Salt Lake, Utah, USA

26. P. Drouet, Rhone, France

27. J. Weber, The University of Wisconsin, Milwakee, WI, USA

28. David C. Kurtz, Rollins College, USA

29. Jorge L. Quiroz, Colima, Mexico

30. Ming-Po Chen, Taiwan, Republic of China

31. Mustafa Telci, Begtepe, Ankara, Turkey

32. Helmut Dietrich, Merseburg, Germany

33. Dong Chen, Fayeteville, Arkansas, USA

34. Mohammad Tabatabai, Cameron University, OK, USA

35. M.S. Khan, Sultan Quboos University, Muscat, Saltanate of Oman

36. Laszlo Mate, Technical University, Budapest, Hungary

37. H.K. Pathak, Bhilai Nayar, India

38. Osvaldo, Pino Garcia, Havana, Cuba

39. B.K. Sharma, Ravishankar University, Raipur, India

40. Aied Al-Knazi, King Abdul Aziz Univ., Jeddah, Saudi Arabia

41. Hassan-Qasin, King Abdul Aziz Univ., Jeddah, Saudi Arabia

42. Tadeusz Jankowski, University Gdansk, Gdansk, Poland

43. K. Kurzak, University Teachers College, Dept. Chemistry, Siedlce, Poland

44. R. Gonzalez, 2000 Rosario, Argentina

45. Emad Fatemi, Ecole Polytechnique Federale de Lausanne, Switzerland

46. Prasad Balusu, University of Rochester, MI, USA

47. Dieter Schott, Rostolki, Germany

48. J.M. Martinez, IMECC-UNICAMP, Brazil

49. Prasad Balusu, India

50. Qun-sheng Zhou, P.R. China

51. W. Kliesch, Universitat Leipzig, Germany

52. Adriana Kindybalyuk, Ukraine Academy of Sciences, Kiev, Ukraine

53. Roman Brovsek, Ljubljana Slovenia

54. D. Mathieu, L.M.R.E., France

55. Donald Schaffner, Rutgers University, NJ, USA

56. David Ward, Barron Associates, Charlottesville, VA, USA

57. Eugene Parker, Barron Associates, Charlottesville, VA, USA

58. Miguel Gomez, Havana, Cuba

59. L. Brueggemann, Leipzig-Halle, Germany

60. Fidel Delgado, Havana, Cuba

61. B.C. Dhage, Maharashtra, India

62. Leida Perea, Havana, Cuba

63. David Ruch, Sam Houston University, Huntsville, Texas

64. Patrick J. Van Fleet, Sam Houston University, Huntsville, Texas

65. Tomas Arechaga, BS. Aires, Argentina

66. M.A. Hernandez, Spain

67. J. Illuateau, Romania

68. Ioan A. Rus, University of Cluj-Napoca, Romania

69. V.K. Jain, Kharagpur, India

70. Alan Lun, University of Melbourne, Victoria, Australia

71. A.M. Saddeek, Assiut University of Mathematics, Assiut, A.R. Egypt

72. Miguel A. Hernandez, Dept. of Mathematics, University de la Rioja, Logrono, Spain

73. James L. Moseley, Dept. of Mathematics, West Virginia University, Morgantown, WV 26500, USA

74. Onesimo Hernandez-Lema, CINVESTAV-IPN, Dept. of Mathematics, D.F. Mexico

75. R.L.V. Gonzalez, Rosario, Argentina

76. Jose A. Ezquerro, Logrono, Spain

77. N. Ramanujam, Bharathidasan University, Tamil Nadu, India

78. Drouet Pierre, Solaize, France

79. Michael Goldberg, Las Vegas, NV, USA

80. Pierre Drouet, Brignai, France

81. Ravishannar, Shukla, Raipur, India

82. W. Quapp, Leipzig, Germany

83. Emil Catinas, Cluj-Napoca, Romania

84. Ion Pavaloiu, Cluj-Napoca, Romania

85. Th. Schauze, Lahn, Germany

86. Ioan Lazar, Cluj-Napoca, Romania

87. Ch. Grossman, Dresden, Germany

88. Livinus, Uko, Medellin, Colombia

89. Z. Athanassov, Bulgarian Academy of Sciences, Sofia, Bulgaria

90. Zhenyu Huang, Nanjing P.R. China

91. John Neuberger, Northern Arizona University, Flagstaff, AZ, USA

92. L.J. Lardy, Syracuse University, Syracuse, NY, USA

93. Kresimir Veselic, Lehrgebiet Mathematische Physik, Hagen, Germany

94. Huang Zhengda, Zhejiang, P.R. China, Columbia University, USA

95. Vasudeva, Murthy, Bangalore, India

96. Adeyeye, S. Johnson C. Smith Univ. NC, USA.

97.Narasimham,Andhra,Pradesh ,India.

98.Marius Heljiu,Univ. Petrosani,Hunedoara,Romania.

99.Nicolae Todor,Oncology institute,Cluj-Napoca,Romania.

100.Pradid Kumar Parida,Kharagpur,India.

101.Nunchun,China.

102.Proinov,Plovdiv, Bulgaria.

103.Babajee Razin,Univ. Mauritius,Mauritius.

104.Dr. Athanasov,Bulgarian Academy of Sciences,Sofia Bulgaria.

105.Dr. Martin Hermann, Friedrisch –ScHilerr Universitat, Jena, Germany.

 

 

(L) Seminars

At the University of Iowa I gave eight seminars per academic year. I continue doing so at New Mexico State and Cameron University ( at an informal basis). During my talks I explain my current work.

 

(M) Papers Presented as an Invited Speaker

1. University of Berkeley, International Summer Institute on Nonlinear Functional Analysis and Applications (1983). Title: "On a contraction theorem and applications".

2. Los Alamos Laboratories (organizers), Conference on Invariant Imbedding, Transport Theory, and Integral Equations, Eldorado Hotel, Santa Fe, NM (1988). Title: "On a class of nonlinear equations arising in neutron transport".

3. Annual Meeting of the American Mathematical Society #863, San Francisco, California, June 16-19, 1991. Title: "On the convergence of algorithmic models" (Chairman of the Numerical Analysis Session (#516), 7:00 p.m. - 9:55 p.m., Thursday, Jan. 17, 1991).

4. Mathematical Association of America, Oklahoma-Arkansas Section, Spring 1991. Title: "Improved bounds for the zeros of polynomials".

5. Annual Meeting of the American Mathematical Society #871, Baltimore, Maryland, Jan. 8-11, 1992. Title: "On the midpoint iterative method for solving nonlinear operator equations in Banach spaces".

6. CAM 92, Edmond, OK, March 27, 1992, University of Central Oklahoma. Title: "On the secant method under weak assumptions".

7. CAM 93, Edmond, OK, February 5, 1993, University of Central Oklahoma. Title: "On a two-point Newton method in Banach spaces of order four and applications".

8. As in (7). Title: "Sufficient convergence conditions for iterations schemes modeled by point-to-set mappings".

9. As in (7). Title: "On a two-point Newton method in Banach spaces and the Ptak error estimates".

10. CAM 94, Edmond, IK, February 4, 1994, University of Central Oklahoma. Title: "On the monotone convergence of fast iterative methods in partially ordered topological spaces".

11. CAM 94, Edmond, OK, February 4, 1994, University of Central Oklahoma. Title: "On a multistep Newton method in Banach spaces and the Ptak error estimates".

12. 56th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical Association of America, March 24, 1994. Title: "On an inequality from applied analysis", (Analysis section). It was held at the University of Searcy, Searcy, Arkansas.

13. CAM 95, Edmond, OK, February 10, 1995, University of Central Oklahoma. Title: "A mesh independence principle for nonlinear equations in Banach spaces and their discretizations".

14. 57th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical Association of America, March 1995, Southwestern Oklahoma State University, Weatherford, Oklahoma. Title: "On the discretization of Newton-like methods".

15. CAM 96, Edmond, OK, February 9, 1996, University of Central Oklahoma. Title: "A unified approach for constructing fast two-step methods in Banach space and their applications".

16. 58th Annual Meeting of the Oklahoma-Arkansas Session of the Mathematical Association of America, March 22--23, 1996, Westark Community College, Fort Smith, Arkansas. Title: "Regions containing solutions of nonlinear equations".

17. Second European Congress of Mathematics, International Conference on Approximation and Optimization (ICAOR), Cluj-Napoca, Romania, July 29-August 1, 1996. Title: "On Newton's method".

18. Regional #919 Meeting "Approximation in Mathematics" of the American Mathematical Society in Memphis, TN, University of Memphis, March 21-22, 1997. Title: "Newton methods on Banach spaces with a convergence structure and applications". A.M.S. Abstract #919-65-93.

19. International Conference on Approximation and Optimization, Cluj-Napoca, Romania, May 26-30, 1998. Title: "Relations between forcing sequences and inexact Newton iterates in Banach space".

20. Colloquium Seminars University of Memphis, March 12, 1999. Title: "Recent Developments in Discretization Studies".

21. Research Day Friday, October 27, 2000, University of Central Oklahoma, Edmond, OK. Poster-Talk title: "Developments on the solution of nonlinear operator equations in Banach space and their discretizations".

22. Oklahoma-Arkansas section of the MAA Oklahoma Christian University, March 30, 2001. Talk title: "On the solution of equations on infinite dimensional spaces". President of Section 1E.

23. Oklahoma Academy of Sciences, 90th Annual Technical Meeting, Nov. 2, 2001. Talk and presentation of a paper, Univ. Cameron.

24. Regional Universities Research Day 2001. Poster Presentation, UCO, Edmond, OK, Nov. 9, 2001.

25. 2nd International Conference on Education of the Sciences and Academic Forum, World Coordinating Council of the Science and Academic Forum (SAF). Gave talk, Thessaloniki, Greece, December 7-8, 2001.

26. Regional Universities Research Day 2002. Abstract and Poster Presentation, UCO, Edmond, OK, October 11, 2002.

27. Academic Festival V, March 27-20, 2003 CU. Abstract and Poster Presenter Academic Conference "Beyond Borders: Globalizations and Human Experience".

28. American Mathematical Society Meeting #988, June 18-21, 2003, Seville, Spain. Presentation of an abstract and a paper.

29. Regional Universities Research Day 2003, Nov. 14, abstract and poster presentation, title: “On Miranda’s Theorem”, UCO, Edmond, OK

30. ANACM 2004, Chalkis, Greece, September 10-14, 2004, organized session called “Newton methods”; given talk entitled “Unifying Newton-like methods”

31. Research Day 2004, UCO October 29, 2004, abstract and poster presentation, title: “On the comparison of Moore and Kantorovich theorem in interval analysis”.

32.Research day 2005,UCO,November 11,2005,Poster and abstact presentation entitled:On the Newton-Kantorovich theorem and interior point methods.

33.Participated:”7th International Conference on Clusters:The HPC Revolution 2006” May 2-4, 2006 OU Norman Oklahoma.

34.Participated in the Supercomputing conference on October 4,2006,OU Norman Oklahoma.

35.Participated in the Supercomputing Conference on Clusters:The HPC Revolution 2006,May2-4,2006,Nornan,Ok,,OU(Organ. Dr. Henry Neeman).

36.Participated in the Supercomputing Conference  ,October 4,2006,Norman ,OK,OU.

37.Research Day 2006,UCO,December 1,2006,rescheduled for April 6,2007,Poster and abstract presentation entitled:On an improved convergence analysis of Newton’s method on Riemannian manifolds .

38.Participated in the Supercomputing Conference :How to build the fastest super-computer in USA twice in one academic year.

October 3,2007,Norman OK,OU.

39.Oklahoma Supercomputing Symposium, October 3,2007:Title:Fastest supercomputer twice in USA  twice in a year ,OU, Norman OK.

40.Research Day 2007, October 2007, Poster Presentation title: Solving nonlinear equations, Edmond OK USO.

41. AMS Annual  Meeting, January 6-9,2008, San Diego California, Invited Speaker, Special Sesssion?Code #SS4A, Title:Global Optimization

and Operations Applications Talk title: On the semilocal convergence of Newton’s Method , Submitted Abstract  Acceptance # 1035-65-357.

42. International Conference celebrating Popoviciu birthday. Cluj-Napoca Romania ,May 6, 2009,Invited speaker,Title: Finding good starting

 points for Newton’s method.

43.Paper presentation Oklahoma Research day 2009, Broken Arrow Oklahoma (given by coauthor Ms Zhao)

     Title:Enclosing roots of polynomials. A talk was also given in the Torus conference ,Wichita Falls Texas,February 27,2010.

44.Paper presentation, Torus Conference, Wichita Falls Texas ,February 27,2010.

45.Poster Presentation, Oklahoma Research Day 2010,CU,Lawton,OK, November 12,2010.

46.Poster Presentation,Oklahome Research Day 2011,CU,Lawton,Ok Novermber,2011.

 

 

(N) Selected Lectures Presented

1. University of Georgia, 1982-1984

2. University of Iowa, 1984-1986

3. State University of Iowa, 1985

4. Northern University of Viginia, 1986, 1988

5. New Mexico State University, 1986-1990

6. University of Ohio, 1986

7. University of Iowa, 1986, 1988

8. University of New York, 1986-1988

9. University of Texas at El Paso, 1987-1990

10. University of Arizona, I.E.D., 1989, 1990

11. Portland State University, 1990

12. Cameron University, 1990

13. University of Central Oklahoma, 1992, 1993, 1994, 1995, 1996

14. University of Cyprus, Nicosia Cyprus, 1993

 

(O) Other Meetings Attended

1. American Mathematical Society/Mathematical Association of America Annual Meetings, Denver, Colorado, 1983, and Phoenix, Arizona, 1989

2. SIAM Mathematical Meetings, Des Moines, Iowa, 1995

3. International Conference on Theory and Applications of Differential Equations, Ohio University, Athens, Ohio, 1988

4. Annual Research Conferences of the Bureau of the Census, Arlington, Virginia, March 21-24, 1993 and 1995.

 

5. TEACHING EXPERIENCE

(A) Courses Taught

Graduate Courses

1. Real Analysis

2. Functional Analysis

3. Operator Theory

4. Numerical Solutions of Ordinary Differential Equations, Partial Differential Equations, Integral Equations, Integral Differential Equations

5. The Finite Difference and the Finite-Element Method for Ordinary Differential Equations and Partial Differential Equations

6. Differential Equations

7. Partial Differential Equations

8. Special Topics in Functional Analysis, Numerical Functional Analysis, and Differential Equations

9. Numerical Solution of Functional Equations

10. Advanced Numerical Analysis

11. Thesis in Mathematics

12. Optimization

 

Undergraduate Courses

1. Functional Analysis

2. Real Analysis

3. Numerical Analysis

4. Differential Equations

5. Linear Algebra

6. History of Mathematics

7. Geometry

8. Statistics

9. Abstract Algebra

10. Independent Study in Mathematics

11. Matrix Algebra

12. Survey of Mathematics

13. Intermediate Algebra, regular and computer guided

14. College Algebra, regular and computer guided

15. Beginning Algebra, regular and computer guided

16.Beginning and Intermediate Algebra

17.Independent Study in Mathematics: Undergraduate Research in Nonlinear Programming and Optimization

18. Calculus 1,2,and 3, and Elementary Calculus

 

(B) Teaching Effectiveness

I believe that I have had some success in using computer software for some of the applied math courses taught in the department. Since my research area is in applied mathematics it was not difficult for me to use existing software as well as produce my own. It has been desirable for students to use computer software as a facilitating tool in many courses.

I have been attending seminars and conferences as well as constantly reviewing the developments in my field in order to have a broad knowledge of mathematical subjects. I am trying to be aware of its increasing relevance in our technological age, and be able to stimulate my students to understand and possibly use some of these concepts in their future careers.

I am also concerned with the communication of these ideas to students. Throughout the course I try to make the concepts as understandable as possible by giving examples that help them relate these ideas to topics in that course. I have also provided opportunities to my students in which they can express their views to the class to sharpen their skills in discovering and communicating the concepts. I have used my teaching effectiveness throughout my teaching career.

I have also produced several textbooks/monographs to be used by students in Mathematics, Economics, Physics, Engineering, and the applied sciences. Several more on the same areas have been submitted.

I have reviewed several undergraduate and graduate textbooks (see 4(C)).I reviewed for example the Numerical Analysis textbook entitled "Introduction to Numerical Analysis", by Kendall Atkinson, University of Iowa, published by John Wiley and Sons (1992). The author in his preface recognizes and praises my talents in teaching and expresses his gratitude for my contribution in the improvement of the book. His textbook is considered to be the best book in Numerical Analysis in this country.

I have assisted several students to be accepted in graduate programs at the top universities in this country.

I have also helped them find jobs and still keep in contact with them and their careers after they leave the University.

 

6. AWARDS, HONORS AND AFFILIATIONS

(A) Conference Chairman

(1)     Applied Mathematics Section Annual Meeting of the American Mathematical Society and Mathematical Association of America meeting, held at San Francisco, January 1991.

(2)     Session organizer conference in Applied Numerical Analysis and Computational Mathematics,Chalkis,Greece,September 10-14,2004,Session title:Newton Methods.

 

(B) Outstanding Graduation Record

I was able to finish both my M.S. and Ph.D. degrees at the University of Georgia at the record time of two years which has not been broken yet.

 

(C) National-International Recognition

(1)     A total of 98 scientists from five continents have requested reprints of  93% of my published works so far.

(2)     I have participated in the evaluation process for tenure and promotion by several U.S. and international universities.

(3)     I reviewed several Ph.D. theses of students from the United States and overseas universities.

(4)     Nominated for the Distinguished Faculty Award for 1993, 1995, and 2001 Cameron University.

(5)     Included in the fourth and consequent editions of "WHO'S WHO AMONG AMERICA'S TEACHERS", 1996. This national organization honors a select 5% of United States teachers.

(6)     Received the Distinguished Research award "medal of excellence" by the Southwest Oklahoma Advanced Technology Association, February 23, 2001 (President Bill Burgess, Mezzanine Shepler Center, Cameron University).

(7)     Nominated for the Faculty Hall of Fame Award, Cameron University, 2001, 2002, 2003.

(8)     Included in the "1000 Great Americans", receiving the medal and plaque by the International Biographical Centre, Cambridge, England.

(9)     Received the Lifetime Achievement Award in Mathematics (medal and plaque) (2001) by the International Biographical Centre, Cambridge, England.

(10) Elected Member of the World Coordinating Council of the Science and Academic Forum (SAF) (Nov. 2001) (11 members worldwide, 4 in U.S.). This forum is advising/assisting the Greek government in academic matters.

(11) Nominated for the "Hackler Award for Teaching", Cameron University, Fall 2002.

(12) Included (2002) in the Strathmore's "Who's Who" and received an award for mathematical contributions.

(13) Received the Academic Initiative Award for 2004-2004 (CU#1661).

(14) Received congratulatory letters from Senators Sam Helton, and Jim Maddox,President Dr. C. Ross, Dean Dr. G. Buckley, Chairman, Dr. T. Tabatabai. 

(15) Elected (2008) to join the “Round Table Group’s Expert Newtwork” This is one of the world’s preeminent consortia of consulting experts based in Washington DC.

(16) Nominated for the CU Research Award,  Spring 2010.

 

7. DEPARTMENTAL SERVICE

1.       Member of the graduate studies committee (N.M.S.U.)

2.       Member of the graduate faculty (N.M.S.U.)

3.       I have been asked and provided input to the members of the departmental personnel committee concerning hiring, updating the math majo,the PQIR,the selection of new books and other matters.

4.       I have been serving as a regular advisor to students and have helped some of them to present papers and give talks at conferences.

5.       Served in the following committees:Hiring,Personnel,Scholarship,Textbook selection for the classes and the CU library.

6.       Administered the Interscholastic and CAAPS tests.

7.       I coauthored the Interscholastic test in Geometry (with Dr. Jankovic).

8.       I have written a 50 Exercises test bank to be used as a source for the upper assessment in mathematics written test.

9.       Wrote letters of reference for 57 students and 17 professors.

10.    Browsing Fair Departmental Represenative,August 2006,and April 28,2007,March 2008,2009,March 6,March 27,and November 6,2010, Cameron University.

11.    Menber of committees :hiring,scholarship,PQIR,book selection,and other .

 

8. UNIVERSITY SERVICE

1.       I have been participating in the Cameron Interscholastic Service.

2.       I have been serving some of the Cameron faculty as consultant.

3.       Dean's representative (N.M.S.U.).

4.       Southwest  Oklahoma Advanced Technology Association Committee Member(2001-Present)

5.       Giving interviews to Lawton Constitution,Cameron Collegian, KCCU TV,and Wichita magazine.

6.       Grievance committee member 2006-2007.

7.       CU Academic Fair representative Music theatre August 2006.

8.       Promotion committee(Chair),Screening Committeee, Scholarship Committee member,2006-2007.

9.       President’s Action Commission on Student Retention Committee Member : Fall 2007- Present.

 

9. COMMUNITY SERVICE

I have been helping people from Lawton (Fort Sill, Goodyear plant and others) and surrounding areas with their mathematical problems.

 

11. COMPUTING EXPERIENCE (LANGUAGES)

(a)     Cobol

(b)     Fortran

(c)     C++

(d)     Java

(e)     Parallel computing

 

12. CLUB MEMBERSHIP

(a)     American Mathematical Society (since 1982)

(b)     Pi Mu Epsilon

(c)     MAA until 2002

(d)     Upsilon Pi Epsilon

 

13. CITATIONS

My papers have been cited by other researchers over 1000 times. An internet search for my name produces over  6,200 cites.

 

14. BRIEF DESCRIPTION OF SOME OF THE BOOKS AS LISTED IN 4 (I)

1. The Theory and Applications of Iteration Methods

This textbook was written for students in engineering, the physical sciences, mathematics, and economics at an upper division undergraduate or graduate level. Prerequisites for using the text are calculus, linear algebra, elements of functional analysis, and the fundamentals of differential equations. Students with some knowledge of the principles of numerical analysis and optimization will have an advantage, since the general schemes and concepts can be easily followed if particular methods, special cases, are already known. However, such knowledge is not essential in understanding the material of this book.

A large number of problems in applied mathematics and also in engineering are solved by finding the solutions of certain equations. For example, dynamic systems are mathematically modeled by differences or differential equations, and their solutions usually represent the states of the systems. For the sake of simplicity, assume that a time-invariant system is driven by the equation x = f(x), where x is the state. Then the equilibrium states are determined by solving the equation f(x) =0. Similar equations are used in the case of discrete systems. The unknowns of engineering equations can be functions (difference, differential, and integral equations), vectors (systems of linear or nonlinear algebraic equations), or real or complex numbers (single algebraic equations with single unknowns). Except in special cases, the most commonly used solution methods are iterative - when starting from one or several initial approximations a sequence is constructed that converges to a solution of the equation. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand. Since all of these methods have the same recursive structure, they can be introduced and discussed in a general framework.

In recent years, the study of general iteration schemes has included a substantial effort to identify properties of iteration schemes that will guarantee their convergence in some sense. A number of these results have used an abstract iteration scheme that consists of the recursive application of a point-to-set mapping. In this book, we are concerned with these types of results.

Each chapter contains several new theoretical results and important applications in engineering, in dynamic economic systems, in input-output systems, in the solution of nonlinear and linear differential equations, and in optimization problems.

Chapter 1 gives an outline of general iteration schemes in which the convergence of such schemes is examined. We also show that our conditions are very general: most classical results can be obtained as special cases and, if the conditions are weakened slightly, then our results may not hold. In Chapter 2 the discrete time-scale Liapunov theory is extended to time dependent, higher order, nonlinear differential equations.

In addition, the speed of convergence is estimated in most cases. The monotone convergence to the solution is examined in Chapter 3 and comparison theorems are proved in Chapter 4. It is also shown that our results generalize well-known classical theorems such as the contraction mapping principle, the lemma of Kantorovich, the famous Gronwall lemma, and the well-known stability theorem of Uzawa. Chapter 5 examines conditions for the convergence of special single-step methods such as Newton's method, modified Newton's method, and Newton-like methods generated by point-to-point mappings in a Banach space setting. The speed of convergence of such methods is examined using the theory of majorants and a method called "continuous induction", which builds on a special variant of Banach's closed graph theorem. Finally, Chapter 6 examines conditions for monotone convergence of special single-step methods such as Newton's method, Newton-like methods, and secant methods generated by point-to-point mappings in a partially ordered space setting.

At the end of each chapter, case studies and numerical examples are presented from different fields of engineering and economy.

 

3. The Theory and Application of Abstract Polynomial Equations

My goal in the text is to present new and important old results about polynomial equations as well as an analysis of general new and efficient iterative methods for their numerical solution in various very general space settings. To achieve this goal we made the text as self-contained as possible by proving all the results in great detail. Exercises have been added at the end of each chapter that complement the material in the sense that most of them can be considered really to be results (theorems, propositions, etc.) that we decided not to include in the main body of each chapter. Several applications of our results are given for the solution of integral as well as differential equations throughout every chapter.

Abstract polynomial equations are evidently systems of algebraic polynomial equations. Polynomial systems can arise directly in applications, or be approximations to equations involving operators having a power series expansion at a certain point. Another source of polynomial systems is the discretization of polynomial equations taking place when a differential or an integral equation is solved. Finite polynomial systems can be obtained by taking a segment of an infinite system, or by other approximation techniques applied to equations in infinite dimensional space.

We have provided material that can be used on the one hand as a required text in the following graduate study areas: Advanced Numerical Analysis, Numerical Functional Analysis, Functional Analysis and Approximation Theory. On the other hand, the text can be recommended for a graduate integral or differential equations course. Moreover, to make the work useful as a reference source, literature citations will be supplied at the end of each chapter with possible extensions of the facts contained here or open problems. We will use graphics and exercises designed to allow students to apply the latest technology. In addition, the text will end with a very updated and comprehensive bibliography in the field. The main prerequisite for the reader is the material covered in: advanced calculus, second course in numerical-functional analysis and a first course in algebra and integral-differential equations. A comprehensive modern presentation of the subject to be described here appears to be needed due to the rapid growth in this field and should benefit not only those working in the field, but also those interested in, or in need of, information about specific results or techniques.

Chapters 1, 2 and 3 cover special cases of nonlinear operator equations. In particular the solution of polynomial operator equations of positive integer degree n is discussed. The so-called polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is most likely due to the fact that unlike polynomials in a single variable, polynomial operators have received little attention. It must certainly be mentioned that existence theory is far from complete and what little is there is confined to local small solutions in neighborhoods which are often of very small radius. Here an attempt is made to partially fill this space by doing the following:

(a)    Numerical methods for approximating distinct solutions of quadratic (n =2) (in Chapters 1 and 2) and polynomial equations (n > 2) (in Chapter 3) are given;

(b)   Results on global existence theorems not related with contractions are provided;

(c)    Moreover for those of a qualitative rather than computational frame of mind, it has been suggested that polynomial operators should carry a Galois theory. In an attempt to inform and contribute in this area we have provided our results at the end of each chapter.

Chapter 4 deals with polynomial integral as well as polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity and other areas. In particular, results on the various Chandrasekhar equations (Nobel Prize of Physics, 1983) are given using Chapters 1-3. These results are demonstrated through the examination of different cases.

In Chapter 5 we study the Weierstrass theorem, Matrix representations, Lagrange and Hermite interpolation, completely continuous multilinear operators, and the bounds of polynomial equations in the following settings: Banach space, Banach algebra and Hilbert space.

Finally in Chapter 6 we provide general methods for solving operator equations. In particular we use inexact Newton-like methods to approximate solutions of nonlinear operator equations in Banach space. We also show how to use these general methods to solve polynomial equations.

 

6. A Survey of Efficient Numerical Methods and Applications

Our goal in this textbook is to present a survey of new, and important old results about equations as well as an analysis of new and efficient iterative methods for their numerical solution in various space settings. To achieve this goal, we made the textbook as self-contained as possible by providing all the results in great detail. Exercises have been added at the end of each chapter that complement the material. Some of them are results (Theorems, Propositions, etc.) that we decided not to include in the main body of each chapter. Several applications of our results are given for the solution of integral as well as differential equations throughout every chapter.

We have provided material that can be used by undergraduate students at their senior year as well as researchers interested in the following study areas: Advanced Numerical Analysis, Numerical Functional Analysis, Functional Analysis Approximation Theory, Integral and Differential Equations, and all computational areas of Engineering, Economics and Statistics. Moreover, we make the work useful as a reference source, literature citations have been supplied at the end of each chapter with possible extensions of the facts contained here or open problems. The exercises are designed to allow readers to apply the latest technology. In addition, the textbook ends with a very updated and comprehensive bibliography in the field. The main prerequisite for the reader is the material covered in: Advanced Calculus, Advanced Course in Analysis, second course in Numerical-Functional Analysis and a first course in Algebra and Integral-Differential Equations. A comprehensive modern presentation of the Numerical Methods described here appears to be needed due to the rapid growth in this field and should benefit not only those working in the area, but also those interested in, or in need of, information about specific results or techniques.

We use: (E) to denote an equation of the form

F(x) = 0 (E)

defined on spaces to be specified each time; (N) denotes Newton's method

x_n+1 = x_n - F'(x_n)^-1 F(x_n) (n > 0), (N)

notation (S) denotes Secant method

x_n+1 = x_n - [x_n, x_n-1]^-1 F(x_n) (n > 0) (S)

whereas by [x_n ,x_{n-1}] we mean [x_n ,x_{n -1};F]; and finally (NL) denotes Newton-like method

x_{n +1}= x_n -A(x_n )^{-1} F(x_n ) (n > 0). (NL)

Chapter 1 serves as an introduction for the rest of the chapters. Topics related with partially ordered topological spaces are covered here. Moreover, divided differences in linear as well as in Banach spaces are being discussed. Furthermore, divided differences, Frechet derivatives, and the relationship between them is being investigated.

Several unpublished results have also been added demonstrating how to select divided differences, Frechet derivatives satisfying Lipschitz conditions or certain new natural monotone estimates similar but not identical to conditions already in the literature of the form, e.g.,

[x,y] < [u,v] for x < u and y < v.

These results are developed, on the one hand because they are needed for the convergence theorems in Chapters 2-4 that follow, and on the other hand because they have an interest of their own.

Chapter 2 deals with the following concern: Applying Newton methods to solve nonlinear operator equations of the form F(x)=0 in a Banach space amounts to calculating two scalar constants and one scalar function over the positive real line. This is due to the fact that conditions on the Frechet-derivative F' of F of the form

|| F' (x) -F'(y)|| < L||x - y||, or ||F'(x) -F'(y)|| < K(r)|| x - y||

or more recently by us ||F'(x +h)-F' (x)|| < A(r,||h||) for all x,y in a certain ball centered at a fixed point x_0, of radius R>0 with 0 < r < R ||h|| < R - r have been used for the convergence analysis to follow. The constants are of the form a = ||F' (x_0 )^{-1}|| and b = ||F'(x_0 )^{-1} F(x_0)||. The task of computing the constants L, a, b as well as the functions K(r) and A(r,t) is carried out for integral operators F in the spaces X =C, L_p (1 < p < infty ) and L_\infty.

After going through the first two chapters, we can undertake the main goal discussed in the rest of the text.

Chapter 3 covers the problem of approximating a locally (or globally) unique solution of the operator equation F(x) =0 in the following settings: Banach space, Banach algebra, Hilbert space, Partially ordered Topological and Euclidean space. In the first four sections, convergence results are given using Newton (N), Secant (S) as well as Newton-like methods (NL) under conditions on the divided differences, Frechet derivatives discussed in the first two chapters. Several results have been provided to improve upon the ones already in the literature by considering cases. The following have been done:

(a) Refined proofs using the same techniques are given;

(b) Different techniques have been applied;

(c) New techniques have been used;

(d) New results have been discovered.

In Section 5 the monotone convergence of methods (N), (S) and (NL) is discussed.

Until Section 5, two classes of convergence theorems are discussed: theorems of essentially Kantorovich-type and global theorems based on monotonicity considerations. In Section 5 however a general unifying structure for the convergence analysis which is strong enough to derive both types of theorems from a basic theorem is discussed.

In Sections 6 and 7 results on rates of convergence as well as Q- and R-orders are being given respectively. Once recent results of others in this area have been discussed, we show how to improve upon them.

Chapter 4 deals with the problem discussed already in Chapter 3, but two-step Newton methods are employed as an attempt to improve upon the order of convergence and achieve the highest possible computational efficiency. The flow of Chapter 3 is followed here also. In most cases the superiority of these over single-step methods is being demonstrated.

 

15. BRIEF DESCRIPTION OF PAPERS AS LISTED IN 4 (J)

The papers concern topics included in the list of research areas listed in 4(J).

The so-called polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many non-linear problems goes unrecognized by researchers. This is most likely due to the fact that unlike polynomials in a single variable, polynomial operators have received little attention. Whether this situation is due to an inherent intractability of these operators or to simple oversight remains to be seen. Hopefully, one should be able to exploit their semi-linear character to wrest more extensive results for these equations than one can obtain in the general non-linear setting.

Examples of equations involving polynomial operators can be found in the literature. My contribution in this area can be found in papers #3, 4, 6-12, 16, 22, 23, 25, 35, 84. Many of the equations of elasticity theory are of this type #3, 4. The problem discussed there pertains to the buckling of a thin shallow spherical shell clamped at the edge and under uniform external pressure.

Some equations in heat transfer, kinetic theory of gases and neutron transport, including the famous S. Chandrasekhar (Nobel in Physics, 1983) integral equation are of quadratic type. Numerical methods for finding small or large solutions of the above equations and their variations as well as results on the number of solutions of the above equations can be found in papers #1-4, 21, 24, 37, 55, 85, 99.

Some pursuit and bending of beams problems can be formulated as polynomial equations. My investigations on such equations can be found in paper #6.

Paper #11 contains results on the study of feedback systems containing an arbitrary finite number of time-varying amplifiers and the study of electromechanical networks containing an arbitrary number of time-varying nonlinear dissipative elements.

Scientists that have worked in this area agree that much work, both of theoretical and computational nature, remains to be done on polynomials in a normed linear space. A summary of some of the remaining problems can be found in my second and third book (see 4(G)).

It must certainly be mentioned that the existence theory is far from complete and what little is there it is confined to local small solutions in neighborhoods which are often of very small radius #1-5, 7-9, 13, 14, 17, 26, 30, 33. In my papers #5, 6, 8, 10, 23, 30, 33, 34, 37, 42, 69, 72, I have provided numerical methods for approximating distinct solutions of polynomial equations under various hypotheses.

As far as I know the above-mentioned authors are the only researchers that have worked on global existence theorems not related with contractions. My contribution in this area is contained in papers #7, 14, 23, 34, 35, 44, 69.

Moreover for those of a qualitative rather than computational frame of mind, it has been suggested that polynomial operators should carry a Galois theory. Such a theory, should it exist, may be very limited, but nonetheless, interesting. The pessimistic note is prompted by the fact that a complete general spectral theory does not exist for polynomial operators. In an attempt to produce such a theory at least the way an analyst understands it, I wrote the relevant papers #18, 23, 34, 35, 45.

The most important iterative procedures for solving nonlinear equations in a Banach space are undoubtedly the so-called Newton-like methods. Indeed, L.V. Kantorovich has given sufficient conditions for the quadratic convergence of Newton's iteration to a locally unique solution of the abstract nonlinear equation in Banach space. His conditions are in some sense the best possible. For the scalar case these conditions coincide with those given earlier by A.I. Ostrowski. Simple sharp apriori estimates were given independently (by different methods) by W.B. Gragg and R.A. Tapia. The method of nondiscrete mathematical induction was used later by V. Ptak, F. Potra, X. Chen, T. Yamamoto, P. Zabrejko, D. Ngyen, I. Moret et al.; this method yields not only sharp apriori estimates but also convergence proofs through the induction theorem. This method, in which the rate of convergence is now a function and not a number, is closely related with the closed graph theorem. My contribution in this area can be found in the papers 19, 20, 31, 40, 44, 50, 51, 57, 60, 61, 63, 65, 68, 70, 81, 82, 83, 89, 90, 92, 95, 96, 97, 101, 125, 129, 145.

One of the basic assumptions for the use of Newton's method is the condition that the Frechet derivative of the nonlinear operator involved be Frechet-differentiable. There are however interesting differential equations and singular integral equations (see, for example, the work of Etzio Venturino) where the nonlinear operator is only Holder continuous. It turns out that the error analysis of Newton-like methods changes dramatically and the results obtained by the above authors do not hold in this setting. My contribution in this area can be found in the papers #19, 20, 31, 32, 38, 63, 68, 71, 100.

Papers #65, 73, 104, 106 deal with the solutions of nonlinear operator equations containing a nondifferentiable term.

Papers #61, 80, 89, 101, 104, 113 deal with the approximation of implicit functions.

Papers #60, 66, 79, 81, 95, 104 deal with projection methods for the approximate solution of nonlinear equations.

Papers #64, 125, 143 deal with iterative procedures for the solution of nonlinear equations in generalized Banach spaces.

Papers #88, 114, 128, 130, 152 deal with inexact iterative procedures.

Papers #54, 56, 67, 98, 124 deal with the solution of nonlinear operator equations and their discretizations in relation with the mesh-independence principle.

Papers #82, 105, 116 deal with the solution of linear and nonlinear perturbed two-point boundary value problems with left, right and interior boundary layers.

I have applied the above numerical methods, in particular Newton's and its variations to concrete integral equations arising in radiative transfer. See, for example, papers #21, 37. Since the numerical solution of integral equations is closed related to compact operators, I tried in the papers #28, 39, 53, 74 to find some results relating numerical methods and compactness. Work on this subject has already been conducted (see, e.g., the work of P. Anselone and K. Atkinson), but the results so obtained are too general or too particular to be used for my purposes.

Papers #91, 121, 131, 132, 133, 138, 140, 149, 153-218 deal with the convergence and error analysis of multipoint iterative methods in Banach spaces.

Paper #103 deals with the introduction of an optimization algorithm based on the gradient projection technique and the Karmarkar's projective scaling method for linear programming.

Paper #123 (statistics) deals with t-estimates of parameters of general nonlinear models in finite dimensional spaces. The method is highly insensitive to outliers. It can also be applied to solve a system of nonlinear equations.

Papers #62, 74, 76, 93, 94, 107, 134, 139 (mathematical economics) deal with the convergence of iteration schemes generated by the recursive application of a point-to-set mapping. Our results have been applied to solve dynamic economic as well as input-output systems.

The rest of the papers involve nondifferentiable operator equations on generalized Banach spaces with a convergence structure and inexact Newton methods, as well as iterative procedures using outer or generalized inverses. Globally convergent inexact Newton methods have also been studied. In particular sufficient conditions have been imposed on the residuals in order to achieve the usual orders of convergence. We have observed that error bounds can be improved and the radius of convergence for Newton's method can be enlarged if the Frechet derivative of the operator involved is sufficiently many times differentiable; the solution of variational and quasivariational inequalities.