International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 956852, 22 pages
Research Article

A New Hybrid Algorithm for a Pair of Quasi- 𝜙 -Asymptotically Nonexpansive Mappings and Generalized Mixed Equilibrium Problems in Banach Spaces

Department of Mathematics, Yibin University, Yibin 644007, China

Received 22 February 2011; Accepted 20 May 2011

Academic Editor: Vittorio Colao

Copyright © 2011 Jinhua Zhu and Shih-Sen 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.


The purpose of this paper is, by using a new hybrid method, to prove a strong convergence theorem for finding a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for a variational inequality problem, and the set of common fixed points for a pair of quasi- 𝜙 -asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.