Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 454181, 23 pages
doi:10.1155/2008/454181
Research Article

Strong Convergence of a Modified Iterative Algorithm for Mixed-Equilibrium Problems in Hilbert Spaces

Xueliang Gao and Yunrui Guo

 Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
Received 8 July 2008; Accepted 1 August 2008

Recommended by Ram U. Verma

Abstract

The purpose of this paper is to study the strong convergence of a modified iterative scheme to find a common element of the set of common fixed points of a finite family of nonexpansive mappings, the set of solutions of variational inequalities for a relaxed cocoercive mapping, as well as the set of solutions of a mixed-equilibrium problem. Our results extend recent results of Takahashi and Takahashi (2007), Marino and Xu (2006), Combettes and Hirstoaga (2005), Iiduka and Takahashi (2005), and many others.