Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 101690, 15 pages
doi:10.1155/2010/101690
Research Article

Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-ϕ-Nonexpansive Mapping and Relatively Nonexpansive Mapping

Min Liu, Shih-Sen Chang, and Ping Zuo

Department of Mathematics, Yibin University, Yibin, Sichuan 644007, China

Received 18 September 2009; Accepted 18 February 2010

Academic Editor: Charles E. Chidume

Copyright © 2010 Min Liu 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 prove a strong convergence theorem for finding a common element of the set of solutions for generalized equilibrium problems, the set of fixed points of a relatively nonexpansive mapping, and the set of fixed points of a quasi-ϕ-nonexpansive mapping in a Banach space by using the shrinking Projection method. Our results improve the main results in S. Takahashi and W. Takahashi (2008) and Takahashi and Zembayashi (2008). Moreover, the method of proof adopted in the paper is different from that of S. Takahashi and W. Zembayashi (2008).