Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 17294, 14 pages
doi:10.1155/2007/17294
Research Article

On the Existence and Convergence of Approximate Solutions for Equilibrium Problems in Banach Spaces

Nan-Jing Huang,1 Heng-You Lan,2 and Kok Lay Teo3

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2Department of Mathematics, Sichuan University of Sciences and Engineering, Zigong, Sichuan 643033, China
3Department of Mathematics and Statistics, Curtin University of Technology, Perth 6102, Australia

Received 15 June 2006; Revised 11 February 2007; Accepted 20 February 2007

Academic Editor: Charles Ejike Chidume

Copyright © 2007 Nan-Jing Huang 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 and study a new class of auxiliary problems for solving the equilibrium problem in Banach spaces. Not only the existence of approximate solutions of the equilibrium problem is proven, but also the strong convergence of approximate solutions to an exact solution of the equilibrium problem is shown. Furthermore, we give some iterative schemes for solving some generalized mixed variational-like inequalities to illuminate our results.