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

Submit your paper
Know more
The week's pick
Responsive image
Enhancing Privacy Preservation: Multi-Attribute Protection with P-Sensitive K-Anonymity

Twinkle Patel Kiran Amin
Random Articles
Reseach Article

Convergence and Stability Results for CR –iterative Procedure using Contractive-like Operators

by Madhu Aggarwal, Renu Chugh, Sanjay Kumars
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 75 - Number 5
Year of Publication: 2013
Authors: Madhu Aggarwal, Renu Chugh, Sanjay Kumars
10.5120/13107-0418

Madhu Aggarwal, Renu Chugh, Sanjay Kumars . Convergence and Stability Results for CR –iterative Procedure using Contractive-like Operators. International Journal of Computer Applications. 75, 5 ( August 2013), 21-27. DOI=10.5120/13107-0418

@article{ 10.5120/13107-0418,
author = { Madhu Aggarwal, Renu Chugh, Sanjay Kumars },
title = { Convergence and Stability Results for CR –iterative Procedure using Contractive-like Operators },
journal = { International Journal of Computer Applications },
issue_date = { August 2013 },
volume = { 75 },
number = { 5 },
month = { August },
year = { 2013 },
issn = { 0975-8887 },
pages = { 21-27 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume75/number5/13107-0418/ },
doi = { 10.5120/13107-0418 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:43:28.787050+05:30
%A Madhu Aggarwal
%A Renu Chugh
%A Sanjay Kumars
%T Convergence and Stability Results for CR –iterative Procedure using Contractive-like Operators
%J International Journal of Computer Applications
%@ 0975-8887
%V 75
%N 5
%P 21-27
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The aim of this paper is to prove weak and strong convergence as well as weak stability results of CR-iterative procedures using contractive-like operators. The results obtained generalize several existing results. An example is also given, using computer programming in C++, to show that CR-iterative procedure converges faster than SP and Noor iterative procedures.

References
  1. A. M. Harder and T. L. Hicks, Stability Results for Fixed Point Iteration Procedures, Math. Japonica, vol. 33, no. 5, (1988), 693-706.
  2. C. O. Imoru and M. O. Olantinwo, On the stability of Picard and Mann iteration processes, Carp. J. Math. , vol. 19, no. 2, (2003), 155-160.
  3. D. R. Sahu and A. Petrusel, Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces, NonlinearAnalysis: Theory,Methods &Applications, vol. 74, no. 17, (2011), 6012–6023.
  4. I. Timis, On the weak stability of Picard iteration for some contractive type mappings, Annals of the University of Craiova Mathematics and Computer Science Series, vol. 37, no. 2, (2010), 106-114.
  5. J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. , vol. 43, (1991), 153-159.
  6. M. A. Noor, New approximation schemes for general variational inequalities, Journal of Mathematical Analysis and Applications, vol. 251 no. 1, (2000), 217-229.
  7. M. O. Olatinwo, Convergence and stability results for some iterative schemes, Acta Universitatis Apulensis, vol. 26, (2011), 225-236.
  8. M. O. Osilike and 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, vol. 30, no. 12, (1999), 1229–1234.
  9. R. Chugh, V. Kumar and S. Kumar, Strong convergence of a new three step iterative scheme in Banach spaces, American Journal of computational mathematics, vol. 2, (2012), 345-357.
  10. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. , vol. 60, (1968), 71-76.
  11. R. P. Agarwal, D. O'Regan, and D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal. , vol. 8, no. 1, (2007), 61-79.
  12. S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrals, Fund. Math. , vol. 3, (1922), 133-181.
  13. S. Ishikawa, Fixed points by a new iteration method, Proc Am Math Soc. , vol. 44, (1974), 147–150.
  14. S. K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci. , vol. 25, (1972), 727-730.
  15. T. Cardinali and P. Rubbioni, A generalization of the Caristi fixed point theorem in metric spaces, Fixed Point Theory, vol. 11, no. 1, (2010), 3-10.
  16. T. Zamifirescu, Fixed point theorems in metric spaces, Arch. Math. , vol. 23, (1972), 292-298.
  17. V. Berinde, On the convergence of the Ishikawa iteration in the class of quasi contractive operators, Acta Mathematica Universitatis Comenianae, vol. 73, no. 1, (2004), 119–126.
  18. V. Berinde, Iterative Approximation of fixed points, Springer Verlag, Lectures Notes in Mathematics, 2007.
  19. W. Phuengrattana and 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, vol. 235, (2011), 3006- 3014.
  20. W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc. , vol. 4, (1953), 506- 510.
Index Terms

Computer Science
Information Sciences

Keywords

Iterative procedure contractive like operators fixed point weak and strong convergence weak stability

Powered by PhDFocusTM