Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 374815, 32 pages
Research Article

A Hybrid Extragradient Viscosity Approximation Method for Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings

Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, Bangkok 10140, Thailand

Received 25 December 2008; Accepted 4 May 2009

Academic Editor: Wataru Takahashi

Copyright © 2009 Chaichana Jaiboon and Poom Kumam. 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.


We introduce a new hybrid extragradient viscosity approximation method for finding the common element of the set of equilibrium problems, the set of solutions of fixed points of an infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problems for β-inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality, which is the optimality condition for a minimization problem. Results obtained in this paper improve the previously known results in this area.