Journal of Applied Mathematics
Volume 2012 (2012), Article ID 580158, 18 pages
http://dx.doi.org/10.1155/2012/580158
Research Article

Algorithms for a System of General Variational Inequalities in Banach Spaces

Jin-Hua Zhu,1 Shih-Sen Chang,2 and Min Liu1

1Department of Mathematics, Yibin University, Sichuan, Yibin 644007, China
2College of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, China

Received 21 December 2011; Accepted 6 February 2012

Academic Editor: Zhenyu Huang

Copyright © 2012 Jin-Hua Zhu 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

The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approximation solvability theorems are proved. The results presented in the paper improve and extend some recent results.