Journal of Applied Mathematics
Volume 2012 (2012), Article ID 506210, 21 pages
http://dx.doi.org/10.1155/2012/506210
Research Article

Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi- 𝜙 -Asymptotically Nonexpansive Mappings in Banach Spaces

Zhaoli Ma,1 Lin Wang,2 and Yunhe Zhao2

1School of Information Engineering, The College of Arts and Sciences, Yunnan Normal University, Kunming, Yunnan 650222, China
2College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan 650221, China

Received 9 February 2012; Accepted 10 April 2012

Academic Editor: Morteza Rafei

Copyright © 2012 Zhaoli Ma 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 introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi- 𝜙 -asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.