Open Access

Common Solutions of an Iterative Scheme for Variational Inclusions, Equilibrium Problems, and Fixed Point Problems

Journal of Inequalities and Applications20082008:720371

DOI: 10.1155/2008/720371

Received: 24 October 2008

Accepted: 6 December 2008

Published: 21 December 2008

Abstract

We introduce an iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings, the set of solutions of an equilibrium problem, and the set of fixed points of a nonexpansive mapping. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. The results in this paper unify, extend, and improve some well-known results in the literature.

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Authors’ Affiliations

(1)
College of Mathematics and Computer Science, Chongqing Normal University
(2)
Department of Finance, National Sun Yat-Sen University
(3)
Department of Applied Mathematics, National Sun Yat-Sen University

Copyright

© Jian-Wen Peng et al. 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.