Journal of Applied Mathematics
Volume 2012 (2012), Article ID 804642, 15 pages
http://dx.doi.org/10.1155/2012/804642
Research Article

A Hybrid Extragradient-Like Method for Variational Inequalities, Equilibrium Problems, and an Infinitely Family of Strictly Pseudocontractive Mappings

Yaqin Wang,1,2 Hongkun Xu,3 and Xiaoli Fang1

1Department of Mathematics, Shaoxing University, Shaoxing 312000, China
2Mathematical College, Sichuan University, Sichuan, Chengdu 610064, China
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan

Received 31 December 2011; Accepted 15 January 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Yaqin Wang 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

The purpose of this paper is to consider a new scheme by the hybrid extragradient-like method for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of solutions of a variational inequality, and the set of fixed points of an infinitely family of strictly pseudocontractive mappings in Hilbert spaces. Then, we obtain a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm. Our results extend and improve the results of Issara Inchan (2010) and many others.