Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 734181, 21 pages
doi:10.1155/2010/734181
Research Article

Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces

L. C. Ceng,1,2 Y. C. Liou,3 and J. C. Yao4

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Scientific Computing Key Laboratory, Shanghai Universities, Shanghai, China
3Department of Information Management, Cheng Shiu University, no.840, Chengcing Road, Niaosong Township, Kaohsiung County 833, Taiwan
4Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan

Received 30 October 2009; Accepted 10 January 2010

Academic Editor: Simeon Reich

Copyright © 2010 L. C. Ceng et al. 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

The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping xn+1=λnxn+(1−λn)(Txn+en)−λnμnF(xn) remains convergent in a Banach space setting where λn,μn∈[0,1], T a nonexpansive mapping, en, n=0,1,…, errors and F a strongly accretive and strictly pseudocontractive mapping.