Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 264052, 10 pages
doi:10.1155/2010/264052
Research Article

General Iterative Algorithm for Nonexpansive Semigroups and Variational Inequalities in Hilbert Spaces

Jinlong Kang,1,2 Yongfu Su,1 and Xin Zhang1

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Foundation, Xian Communication Institute, Xian 710106, China

Received 24 October 2009; Revised 26 December 2009; Accepted 12 February 2010

Academic Editor: Jong Kim

Copyright © 2010 Jinlong Kang 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.

Abstract

We introduce a general iterative method for finding the solution of the variational inequality problem over the fixed point set of a nonexpansive semigroup in a Hilbert space. We prove that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions. Our results improve and generalize many known corresponding results.