Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 230304, 22 pages
doi:10.1155/2010/230304
Research Article

Strong Convergence Theorems for a Generalized Equilibrium Problem with a Relaxed Monotone Mapping and a Countable Family of Nonexpansive Mappings in a Hilbert Space

Shenghua Wang,1 Giuseppe Marino,2 and Fuhai Wang1

1School of Applied Mathematics and Physics, North China Electric Power University, Baoding 071003, China
2Dipartimento di Matematica, Universitá della Calabria, 87036 Arcavacata di Rende, Italy

Received 15 March 2010; Accepted 20 June 2010

Academic Editor: Naujing Jing Huang

Copyright © 2010 Shenghua Wang et al. 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 a new iterative method for finding a common element of the set of solutions of a generalized equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings in a Hilbert space and then prove that the sequence converges strongly to a common element of the two sets. Using this result, we prove several new strong convergence theorems in fixed point problems, variational inequalities, and equilibrium problems.