Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 567147, 20 pages
doi:10.1155/2009/567147
Research Article

A Viscosity Approximation Method for Finding Common Solutions of Variational Inclusions, Equilibrium Problems, and Fixed Point Problems in Hilbert Spaces

Somyot Plubtieng1,2 and Wanna Sriprad1,2

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2PERDO National Centre of Excellence in Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand

Received 12 February 2009; Accepted 18 May 2009

Academic Editor: William A. Kirk

Copyright © 2009 Somyot Plubtieng and Wanna Sriprad. 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.

Abstract

We introduce an iterative method for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of a variational inclusion with set-valued maximal monotone mapping, and inverse strongly monotone mappings and the set of solutions of an equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper improve and extend the main results of J. W. Peng et al. (2008) and many others.