Abstract and Applied Analysis
Volume 2011 (2011), Article ID 701675, 27 pages
http://dx.doi.org/10.1155/2011/701675
Research Article

Strong Convergence Theorems for Countable Families of Uniformly Quasi- 𝜙 -Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems

Siwaporn Saewan and Poom Kumam

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, Thailand

Received 24 March 2011; Accepted 30 May 2011

Academic Editor: Yuming Shi

Copyright © 2011 Siwaporn Saewan and Poom Kumam. 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 present a new hybrid block iterative scheme by the generalized 𝑓 - projection method for finding a common element of the fixed point set for a countable family of uniformly quasi- 𝜙 -asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature.