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  • Research Article
  • Open Access

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

Journal of Inequalities and Applications20082008:454181

https://doi.org/10.1155/2008/454181

  • Received: 8 July 2008
  • Accepted: 1 August 2008
  • Published:

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.

Keywords

  • Hilbert Space
  • Variational Inequality
  • Recent Result
  • Iterative Algorithm
  • Nonexpansive Mapping

Publisher note

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Authors’ Affiliations

(1)
Department of Mathematics, Sichuan University, Chengdu, Sichuan, 610064, China

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.

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