Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 945051, 24 pages
Research Article

A Viscosity of Cesàro Mean Approximation Methods for a Mixed Equilibrium, Variational Inequalities, and Fixed Point Problems

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

Received 6 September 2010; Accepted 15 October 2010

Academic Editor: Qamrul Hasan Ansari

Copyright © 2011 Thanyarat Jitpeera 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.


We introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a β-inverse-strongly monotone mapping, and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Cesàro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang (2009), Peng and Yao (2009), Shimizu and Takahashi (1997), and some authors.