Copyright © 2010 Jintana Joomwong. 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 for finding a common element of infinitely nonexpansive mappings, the set of solutions of a mixed equilibrium problems, and the set of solutions of the variational inequality for an α-inverse-strongly monotone mapping in a Hilbert Space. Then, the strong converge theorem is proved under some parameter controlling conditions. The results of this paper extend and improve the results of Jing Zhao and Songnian He(2009) and many others. Using this theorem, we obtain some interesting corollaries.