Journal of Applied Mathematics
Volume 2012 (2012), Article ID 154968, 21 pages
http://dx.doi.org/10.1155/2012/154968
Research Article

A New Iterative Scheme for Solving the Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces

Rabian Wangkeeree1,2 and Pakkapon Preechasilp1

1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 13 February 2012; Accepted 31 March 2012

Academic Editor: Zhenyu Huang

Copyright © 2012 Rabian Wangkeeree and Pakkapon Preechasilp. 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 the new iterative methods for finding a common solution set of monotone, Lipschitz-type continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space. The main result extends various results existing in the current literature.