Table of Contents
ISRN Mathematical Analysis
Volume 2011 (2011), Article ID 687184, 9 pages
http://dx.doi.org/10.5402/2011/687184
Research Article

Robustness of Krasnoselski-Mann's Algorithm for Asymptotically Nonexpansive Mappings

1Department of Mathematics, Nanchang University, Nanchang 330031, China
2Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China

Received 22 February 2011; Accepted 11 April 2011

Academic Editors: V. Kravchenko and A. Peris

Copyright © 2011 Yu-Chao Tang and Li-Wei Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Iterative approximation of fixed points of nonexpansive mapping is a very active theme in many aspects of mathematical and engineering areas, in particular, in image recovery and signal processing. Because the errors usually occur in few places, it is necessary to show that whether the iterative algorithm is robust or not. In the present work, we prove that Krasnoselski-Mann's algorithm is robust for asymptotically nonexpansive mapping in a Banach space setting. Our results generalize the corresponding results existing in the literature.