Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 869684, 14 pages
doi:10.1155/2010/869684
Research Article

Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces

Shih-sen Chang,1 Jong Kyu Kim,2 and Xiong Rui Wang1

1Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China
2Department of Mathematics Education, Kyungnam University Masan, Kyungnam 631-701, South Korea

Received 20 October 2009; Accepted 28 December 2009

Academic Editor: Yeol J. E. Cho

Copyright © 2010 Shih-sen Chang 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 use the modified block iterative method to propose an algorithm for solving the convex feasibility problems for an infinite family of quasi-ϕ-asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.