Research Article
Some Convergence Results for Modified S-Iterative Scheme in Hyperbolic Spaces
|
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
|
| Volume 80 - Issue 6 |
| Published: October 2013 |
| Authors: Renu Chugh, Preety, Madhu Aggarwal |
10.5120/13865-1722
|
Renu Chugh, Preety, Madhu Aggarwal . Some Convergence Results for Modified S-Iterative Scheme in Hyperbolic Spaces. International Journal of Computer Applications. 80, 6 (October 2013), 20-23. DOI=10.5120/13865-1722
@article{ 10.5120/13865-1722,
author = { Renu Chugh,Preety,Madhu Aggarwal },
title = { Some Convergence Results for Modified S-Iterative Scheme in Hyperbolic Spaces },
journal = { International Journal of Computer Applications },
year = { 2013 },
volume = { 80 },
number = { 6 },
pages = { 20-23 },
doi = { 10.5120/13865-1722 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2013
%A Renu Chugh
%A Preety
%A Madhu Aggarwal
%T Some Convergence Results for Modified S-Iterative Scheme in Hyperbolic Spaces%T
%J International Journal of Computer Applications
%V 80
%N 6
%P 20-23
%R 10.5120/13865-1722
%I Foundation of Computer Science (FCS), NY, USA
Abstract
The aim of this paper is to prove strong and ?-convergence theorems of modified S-iterative scheme for asymptotically quasi-nonexpansive mapping in hyperbolic spaces. The results obtained generalize several results of uniformly convex Banach spaces and CAT(0) spaces.
References
- A. R. Khan, H. Fukhar-ud-din and M. A. Khan: An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl. , vol. 54, (2012), 12 pages.
- H. F. Senter and W. G. Dotson: Approximating fixed points of nonexpansive mappings, Proc. Amer. Math. Soc. , vol. 44, (1974), 375–380.
- J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Austral. Math. Soc. , vol. 43, (1991), 153-159.
- K. K. Tan and H. K. Xu: Approximating fixed points of nonexpansive mappings by Ishikawa iteration process, J, Math. Anal. , vol. 178, (1993), 301-308.
- 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.
- L. Leustean: Nonexpansive iterations in uniformly convex W-hyperbolic spaces, Contemp. Math. , vol. 513, (2010), 193-210.
- T. Kuczumow: An almost convergence and its applications, Ann. Univ. Mariae Curie-Sklodowska, Sect. A. , vol. 32, (1978),79-88.
- T. Shimizu and W. Takahashi: Fixed points of multivalued mappings in certain convex metric spaces, Topol. Methods Nonlinear Anal. , vol. 8, (1996), 197-203.
- U. Kohlenbach: Some logical metatheorems with applications in functional analysis, Trans. Amer. Math. Soc. , vol. 357(2005), 89-128.
- W. Kirk and B. Panyanak: A concept of convergence in geodesic spaces, Nonlinear Anal. , vol. 68, (2008), 3689-3696.
- W. Takahashi: A convexity in metric spaces and nonexpansive mapping, Kodai Math. Sem. Rep. , vol. 22, (1970), 142-149.
Index Terms
Keywords