Open Access

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

Journal of Inequalities and Applications20082008:454181

DOI: 10.1155/2008/454181

Received: 8 July 2008

Accepted: 1 August 2008

Published: 3 August 2008

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Sichuan University

Copyright

© X. Gao and Y. Guo. 2008

This article is published under license to BioMed Central Ltd. 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.