Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 454181, 23 pages
Strong Convergence of a Modified Iterative Algorithm for Mixed-Equilibrium Problems in Hilbert Spaces
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
Received 8 July 2008; Accepted 1 August 2008
Academic Editor: Ram U. Verma
Copyright © 2008 Xueliang Gao and Yunrui Guo. 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.
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.