Abstract and Applied Analysis
Volume 2012 (2012), Article ID 498487, 12 pages
http://dx.doi.org/10.1155/2012/498487
Research Article

A Strong Convergence Theorem for Relatively Nonexpansive Mappings and Equilibrium Problems in Banach Spaces

Mei Yuan,1 Xi Li,2 Xue-song Li,2 and John J. Liu3

1Leshan College of Profession and Technology, Sichuan, Leshan 614000, China
2Department of Mathematics, Sichuan University, Sichuan, Chengdu 610064, China
3College of Business, City University of Hong Kong, Hong Kong

Received 3 July 2012; Revised 24 August 2012; Accepted 24 August 2012

Academic Editor: Yeong-Cheng Liou

Copyright © 2012 Mei Yuan 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

Relatively nonexpansive mappings and equilibrium problems are considered based on a shrinking projection method. Using properties of the generalized f-projection operator, a strong convergence theorem for relatively nonexpansive mappings and equilibrium problems is proved in Banach spaces under some suitable conditions.