Abstract and Applied Analysis
Volume 2012 (2012), Article ID 893635, 17 pages
http://dx.doi.org/10.1155/2012/893635
Research Article

Some Results on an Infinite Family of Nonexpansive Mappings and an Inverse-Strongly Monotone Mapping in Hilbert Spaces

Peng Cheng1 and Anshen Zhang2

1School of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2No. 13 Zhongxue, Feng-Feng Kuangqu, Hangdan 056000, China

Received 8 September 2012; Accepted 10 October 2012

Academic Editor: Xiaolong Qin

Copyright © 2012 Peng Cheng and Anshen Zhang. 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 study the problem of approximating a common element in the common fixed point set of an infinite family of nonexpansive mappings and in the solution set of a variational inequality involving an inverse-strongly monotone mapping based on a viscosity approximation iterative method. Strong convergence theorems of common elements are established in the framework of Hilbert spaces.