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