Abstract and Applied Analysis
Volume 2012 (2012), Article ID 147915, 16 pages
http://dx.doi.org/10.1155/2012/147915
Research Article

Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi- 𝝓 -Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces

J. F. Tan1 and S. S. Chang2

1Department of Mathematics, Yibin University, Yibin 644007, China
2College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China

Received 30 December 2011; Accepted 2 February 2012

Academic Editor: Khalida Inayat Noor

Copyright © 2012 J. F. Tan and S. S. Chang. 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 main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi- 𝜙 -asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors.