International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 734082, 22 pages
doi:10.1155/2011/734082
Research Article

Strong Convergence Theorems for Family of Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems and Variational Inequality Problems

Mathematics Institute, African University of Science and Technology, Abuja, Nigeria

Received 20 October 2010; Revised 5 January 2011; Accepted 8 February 2011

Academic Editor: A. Zayed

Copyright © 2011 Yekini Shehu. 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 scheme by hybrid method for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings, the set of common solutions to a system of generalized mixed equilibrium problems, and the set of solutions to a variational inequality problem in a real Hilbert space. We then prove strong convergence of the scheme to a common element of the three sets. We give some applications of our results. Our results extend important recent results.