Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 251510, 14 pages
Research Article

Existence Results for System of Variational Inequality Problems with Semimonotone Operators

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 14 July 2010; Accepted 29 October 2010

Academic Editor: Józef Banaś

Copyright © 2010 Somyot Plubtieng and Kamonrat Sombut. 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.


We introduce the system of variational inequality problems for semimonotone operators in reflexive Banach space. Using the Kakutani-Fan-Glicksberg fixed point theorem, we obtain some existence results for system of variational inequality problems for semimonotone with finite-dimensional continuous operators in real reflexive Banach spaces. The results presented in this paper extend and improve the corresponding results for variational inequality problems studied in recent years.