Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 482869, 22 pages
http://dx.doi.org/10.5402/2012/482869
Research Article

Hybrid Projection Algorithm for a New General System of Variational Inequalities in Hilbert Spaces

1Department of Mathematics and Statistics, Faculty of Science, Thaksin University, Phatthalung Campus, Phatthalung 93110, Thailand
2Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand

Received 5 November 2012; Accepted 18 December 2012

Academic Editors: I. K. Argyros, H. Y. Chung, and Y.-G. Zhao

Copyright © 2012 S. Imnang. 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

A new general system of variational inequalities in a real Hilbert space is introduced and studied. The solution of this system is shown to be a fixed point of a nonexpansive mapping. We also introduce a hybrid projection algorithm for finding a common element of the set of solutions of a new general system of variational inequalities, the set of solutions of a mixed equilibrium problem, and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Several strong convergence theorems of the proposed hybrid projection algorithm are established by using the demiclosedness principle. Our results extend and improve recent results announced by many others.