Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 276859, 10 pages
doi:10.1155/2011/276859
Research Article

An Implicit Iteration Method for Variational Inequalities over the Set of Common Fixed Points for a Finite Family of Nonexpansive Mappings in Hilbert Spaces

Nguyen Buong1 and Nguyen Thi Quynh Anh2

1Vietnamese Academy of Science and Technology, Institute of Information Technology, 18, Hoang Quoc Viet, Cau Giay, Ha Noi 122100, Vietnam
2Department of Information Technology, Thai Nguyen National University, Thainguye 842803, Vietnam

Received 17 December 2010; Accepted 7 March 2011

Academic Editor: Jong Kim

Copyright © 2011 Nguyen Buong and Nguyen Thi Quynh Anh. 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 implicit iteration method for finding a solution for a variational inequality involving Lipschitz continuous and strongly monotone mapping over the set of common fixed points for a finite family of nonexpansive mappings on Hilbert spaces.