Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Copyright © 2009 Rabian Wangkeeree and Uthai Kamraksa. 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 an iterative scheme for finding a common element of the set of common fixed
points of a family of infinitely nonexpansive mappings, and the set of solutions of the variational inequality for an
inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions, some strong convergence theorems
for approximating a common element of the above two sets are obtained. As applications, at the end of the paper we
utilize our results to study the problem of finding a common element of the set of fixed points of a family of infinitely
nonexpansive mappings and the set of fixed points of a finite family of -strictly pseudocontractive mappings. The
results presented in the paper improve some recent results of Qin and Cho (2008).