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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 215261, 17 pages
http://dx.doi.org/10.1155/2012/215261
Research Article

Modified Hybrid Block Iterative Algorithm for Uniformly Quasi- 𝜙 -Asymptotically Nonexpansive Mappings

Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China

Received 6 June 2012; Accepted 11 July 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Qiansheng Feng 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

Saewan and Kumam (2010) have proved the convergence theorems for finding the set of solutions of a general equilibrium problems and the common fixed point set of a family of closed and uniformly quasi- 𝜙 -asymptotically nonexpansive mappings in a uniformly smooth and strictly convex Banach space E with Kadec-Klee property. In this paper, authors prove the convergence theorems and do not need the Kadec-Klee property of Banach space and some other conditions used in the paper of S. Saewan and P. Kumam. Therefore, the results presented in this paper improve and extend some recent results.