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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 178053, 9 pages
http://dx.doi.org/10.1155/2013/178053
Research Article

A New Iterative Method for Equilibrium Problems and Fixed Point Problems

1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Mazandaran University of Science and Technology, Behshahr, Iran

Received 31 October 2013; Accepted 15 December 2013

Academic Editor: Ljubomir B. Ćirić

Copyright © 2013 Abdul Latif and Mohammad Eslamian. 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

Introducing a new iterative method, we study the existence of a common element of the set of solutions of equilibrium problems for a family of monotone, Lipschitz-type continuous mappings and the sets of fixed points of two nonexpansive semigroups in a real Hilbert space. We establish strong convergence theorems of the new iterative method for the solution of the variational inequality problem which is the optimality condition for the minimization problem. Our results improve and generalize the corresponding recent results of Anh (2012), Cianciaruso et al. (2010), and many others.