CFP last date
20 January 2025
Call for Paper
February Edition
IJCA solicits high quality original research papers for the upcoming February edition of the journal. The last date of research paper submission is 20 January 2025

Submit your paper
Know more
The week's pick
Responsive image
SFLA-Based Line Balancing and Task Optimization in Master-Slave Controlled Hanger Transportation Systems for Garment Production

Duc Hoang Nguyen
Random Articles
Reseach Article

Convergence of CR Iterative Scheme with Errors using Quasi-Contractive Operators

by Meenakshi Gugnani, Renu Chugh
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 83 - Number 11
Year of Publication: 2013
Authors: Meenakshi Gugnani, Renu Chugh
10.5120/14490-1572

Meenakshi Gugnani, Renu Chugh . Convergence of CR Iterative Scheme with Errors using Quasi-Contractive Operators. International Journal of Computer Applications. 83, 11 ( December 2013), 5-8. DOI=10.5120/14490-1572

@article{ 10.5120/14490-1572,
author = { Meenakshi Gugnani, Renu Chugh },
title = { Convergence of CR Iterative Scheme with Errors using Quasi-Contractive Operators },
journal = { International Journal of Computer Applications },
issue_date = { December 2013 },
volume = { 83 },
number = { 11 },
month = { December },
year = { 2013 },
issn = { 0975-8887 },
pages = { 5-8 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume83/number11/14490-1572/ },
doi = { 10.5120/14490-1572 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:59:04.174640+05:30
%A Meenakshi Gugnani
%A Renu Chugh
%T Convergence of CR Iterative Scheme with Errors using Quasi-Contractive Operators
%J International Journal of Computer Applications
%@ 0975-8887
%V 83
%N 11
%P 5-8
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The aim of this article is to introduce a new iterative scheme namely CR iterative scheme with errors and prove a general convergence theorem to approximate the unique common fixed point of three operators satisfying a certain contractive condition in an arbitrary Banach space using this newly introduced iterative scheme. An example showing the validity of our results is provided. Comparative analysis of new iterative scheme with already existing iterative schemes is also shown using programming in C++.

References
  1. Agarwal, R. P. , Cho, Y. J. , Li, J. and Huanj, N. J. , Stability of iterative procedures with errors approximating fixed points for a couple of quasi-contractive operators in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. , 272(2002), 435-447.
  2. Berinde, V. , Iterative Approximation of Fixed Points, Editura Efemeride (2007).
  3. Berinde, V. , On the convergence of Ishikawa iterative in the class of quasi- contractive operators, Acta Math. Univ. Comenianae, Vol LXXIII, 1(2004), 119-126.
  4. Chugh, R. Kumar, V. , Convergence of SP iterative scheme with mixed errors for accretive Lipschitzian and strongly accretive Lipschitzian operators in Banach space, Int. J. Of Computer Mathematics, Vol 2013, 17 pages.
  5. Chugh, R. , Kumar, V. , Strong convergence of a new three step iterative scheme in Banach spaces, American Journal of Computational Mathematics, 2( 2012), 345-357.
  6. Goebel, K. and Kirk, W. A. , A fixed point theorem for asymptotically nonexpansive mappings, Proceeding of American mathematical society, Vol 35(1972), 171-174.
  7. Ishikawa, S. , Fixed Point by a New Iterative Method, Proc. Amer. Math. Soc. 44 (1) (1974), 147-150.
  8. Khan, S. H. , Common fixed points of two quasi-contractive operators in normed spaces by iteration, Int. Journal of Math. Analysis,Vol3,3 (2009), 145- 151.
  9. Liu, L. , Fixed Points of local Strictly Pseudo-contractive Mappings Using Mann and Ishikawa iterative with Errors, Indian J. Pure Appl. Math. 26 (7) (1995), 649- 659.
  10. Liu, L. , Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Mappings in Banach Spaces, J. Math. Anal. Appl. 194 (1995), 114-125.
  11. Mann, W. R. , Mean value methods in iteration, Proc. Amer. Math. Soc. , 4(1953),
  12. 506-510.
  13. Noor, M. A. , New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, 251(1)(2004), 217-229.
  14. Olaleru, J. O. , On the convergence of the Mann iterative in locally convex spaces, Carpathian Journal of Mathematics, 22(1-2)(2006), 115-120.
  15. Rafiq, A. , A Convergence Theorem for Mann Fixed Point Iterative Procedure, Applied Mathematics E-Notes 6 (2006), 289-293.
  16. Rashwan, R. A. , Rafiq, A. and Hakim, A. : On the convergence of three-step iterative process with errors in the classs of quasi-contractive operators, Proc. Pakistan Acad. Sci. 46(1) (2009), 41-46.
  17. Rhoades, B. E. , Some Fixed Point Iterative Procedures, Int. J. Math. Math. Sci. , 14 (1) (1991), 1-16.
  18. Rhoades, B. E. , Comments On Two Fixed Point Iterative Methods, J. Math. Anal. Appl. 56 (2) (1976), 741-750.
  19. Thianwan, S. , Common fixed points of new iterations for two asymptotically nonexpansive nonself mappings in Banach spaces, Journal of Computational and Applied Mathematics, 2009,688 -695.
  20. Xu, Y. , Ishikawa and Mann iterative process with errors for non-linear accretive operator equations , J. Math. Appl. 224(1998), 91-101.
  21. Zamfirescu, T. , Fix Point Theorems in Metric Spaces, Arch. Math. 23 (1972), 292- 298.
  22. Zeidler, E. , Nonlinear Functional Analysis and its Applications, Fixed-Point Theorems I. , Springer-Verlag, New York, Inc. (1986).
Index Terms

Computer Science
Information Sciences

Keywords

CR Iterative Scheme Quasi-contractive Operators.

Powered by PhDFocusTM