Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 29091, 10 pages
doi:10.1155/2007/29091
Research Article

Iteration Scheme with Perturbed Mapping for Common Fixed Points of a Finite Family of Nonexpansive Mappings

Yeong-Cheng Liou,1 Yonghong Yao,2 and Rudong Chen2

1Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
2Department of Mathematics, Tianjin Polytechnic University, Tianji 300160, China

Received 17 December 2006; Revised 6 February 2007; Accepted 6 February 2007

Academic Editor: Hélène Frankowska

Copyright © 2007 Yeong-Cheng Liou 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

We propose an iteration scheme with perturbed mapping for approximation of common fixed points of a finite family of nonexpansive mappings {Ti}i=1N. We show that the proposed iteration scheme converges to the common fixed point x*∈ ⋂i=1NFix(Ti) which solves some variational inequality.