CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Data Dependence of Some New Iterative Schemes for Quasi-Contractive Operators

by Renu Chugh, Sanjay Kumar, Jagjeet
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 73 - Number 1
Year of Publication: 2013
Authors: Renu Chugh, Sanjay Kumar, Jagjeet
10.5120/12704-9499

Renu Chugh, Sanjay Kumar, Jagjeet . Data Dependence of Some New Iterative Schemes for Quasi-Contractive Operators. International Journal of Computer Applications. 73, 1 ( July 2013), 12-18. DOI=10.5120/12704-9499

@article{ 10.5120/12704-9499,
author = { Renu Chugh, Sanjay Kumar, Jagjeet },
title = { Data Dependence of Some New Iterative Schemes for Quasi-Contractive Operators },
journal = { International Journal of Computer Applications },
issue_date = { July 2013 },
volume = { 73 },
number = { 1 },
month = { July },
year = { 2013 },
issn = { 0975-8887 },
pages = { 12-18 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume73/number1/12704-9499/ },
doi = { 10.5120/12704-9499 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:38:53.092626+05:30
%A Renu Chugh
%A Sanjay Kumar
%A Jagjeet
%T Data Dependence of Some New Iterative Schemes for Quasi-Contractive Operators
%J International Journal of Computer Applications
%@ 0975-8887
%V 73
%N 1
%P 12-18
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper we prove data dependence of new multistep iterative scheme as well as CR iterative scheme for quasi contractive operators, that is, by using an approximate quasi -contractive operator we approximate the fixed point of the given operators.

References
  1. Agarwal, R. P. , O'Regan, D. and Sahu, D. R. : Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, Journal of Nonlinear and Convex Analysis 8(1) (2007), 61-79.
  2. B. E. Rhoades, S. M. Soltuz, "The equivalence between Mann-Ishikawa iterations and multi-step iteration", Nonlinear Analysis, 58(2004), 219-228.
  3. C. O. Imoru, M. O. Olantiwo, "On the stability of Picard and Mann iteration processes", Carpathian Journal of Mathematics, 19(2003), no. 2, 155-160.
  4. Chifu, G. Petru¸sel, "Existence and Data Dependence of Fixed Points and Strict Fixed Points for Contractive-Type Multivalued Operators", Fixed Point Theory and Applications, 2007(2007), Article ID 034248, 8 pages.
  5. F. Gursoy et al. , "Data dependence results of new multi-step and s-iterative schemes for contractive-like operators", Fixed Point Theory and Application, 10. 1186/1687-1812-2013-76.
  6. I. A. Rus, A. Petru¸sel, A. Sˆ?ntamarian,"Data dependence of the fixed points set of multivalued weakly Picard operators", Stud. Univ. Babes-Bolyai, Math. 46 (2) (2001) 111-121.
  7. I. A. Rus, A. Petru¸sel, A. Sˆ?ntamarian, "Data dependence of the fixed point set of some multivalued weakly Picard operators", Nonlinear Analysis: Theory, Methods & Applications, 52 (2003), 1947–1959
  8. I. A. Rus, S. Muresan,"Data dependence of the fixed points set of weakly Picard operators", Stud. Univ. Babes-Bolyai 43 (1998) 79-83.
  9. J. O. Olaleru, H. Akewe," On multistep iterative scheme for approximating the common fixed points of contractive-like operators", Int. Journal of Mathematics and mathematical sciences. Volume 2010, Article ID 530964, 11 pages
  10. J. T. Markin,"Continuous dependence of fixed point sets", Proc. AMS 38 (1973) 545-547.
  11. M. O. Olatinwo,"On the continuous dependence of the fixed points for ( )-contractive-type operators", Kragujevac Journal of Mathematics, 34(2010), 91-102.
  12. M. O. Olatinwo,"Some results on the continuous dependence of the fixed points in normed linear space", Fixed Point Theory, 10(2009), no. 1, 151-157.
  13. M. A. Noor,"New approximation schemes for general variational inequalities", Journal of Mathematical Analysis and Applications, 251(2000), no. 1, 217-229.
  14. M. O. Osilike, A. Udomene, "Short proofs of stability results for fixed point iteration procedures for a class of contractive-type mappings", Indian Journal of Pure and Applied Mathematics, 30(1999), no. 12, 1229-1234.
  15. R. Chugh, V. Kumar, "Data dependence of Noor and SP iterative schemes when dealing with quasi-contractive operators", International Journal of Computer Applications, 31(2011), no. 5.
  16. R. Chugh, V. Kumar, S. Kumar,"Strong convergence of a new three step iterative scheme in Banach spaces", American Journal of Computational Mathematics, 2(2012), 345-357.
  17. R. Esp´?nola, A. Petru¸sel,"Existence and data dependence of fixed points for multivalued operators on gauge spaces", J. Math. Anal. Appl. , 309 (2005), 420–432.
  18. S. Ishikawa,"Fixed points by a new iteration method", Proc. Amer. Math. Soc. , 44(1974), 147-150.
  19. S. M. Soltuz,"Data dependence for Ishikawa iteration", Lecturas Mathematicas, 25(2004), no. 2, 149-155.
  20. S. M. Soltuz, "Data dependence for Mann iteration", Octogon Math. Magazine, 9(2001), 825-828.
  21. S. M. Soltuz, T. Grosan,"Data dependence for Ishikawa iteration when dealing with contractive like operators", Fixed Point Theory and Applications, 2008(2008), Article ID 242916, 7 pages.
  22. T. Zamfirescu,"Fixed point theorems in metric spaces", Archiv der Mathematik, 23(1972), no. 1, 292-298.
  23. V. Berinde,"Iterative Approximation of Fixed Points ", Springer, Berlin (2007).
  24. V. Berinde,"On the approximation of fixed points of weak contractive mappings", Carpathian J. Math. , 19(2003), no. 1, 7-22.
  25. W. Phuengrattana, S. Suantai,"On the rate of convergence of Mann, Ishikawa, Noor and SP iterations for continuous functions on an arbitrary interval", Journal of Computational and Applied Mathematics, 235(2011), 3006-3014.
  26. W. Takahashi,"Iterative methods for approximation of fixed points and their applications", Journal of the Operations Research Society of Japan, 43(2000), no. 1, 87-108.
  27. W. R. Mann, "Mean value methods in iterations", Proc. Amer. Math. Soc. , 4(1953), 506-510.
  28. Xu, M. A. Noor, "Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations", J. Math. Anal. Appl. , 224(1998), 91-101
Index Terms

Computer Science
Information Sciences

Keywords

CR Iteration Data Dependence New Multistep Iteration Quasi Contractive

Powered by PhDFocusTM