Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 904320, 19 pages
doi:10.1155/2011/904320
Research Article

The Existence of Maximum and Minimum Solutions to General Variational Inequalities in the Hilbert Lattices

Jinlu Li1 and Jen-Chih Yao2

1Department of Mathematics, Shawnee State University, Portsmouth, OH 45662, USA
2Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804-24, Taiwan

Received 24 November 2010; Accepted 8 December 2010

Academic Editor: Qamrul Hasan Ansari

Copyright © 2011 Jinlu Li and Jen-Chih Yao. 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 apply the variational characterization of the metric projection to prove some results about the solvability of general variational inequalities and the existence of maximum and minimum solutions to some general variational inequalities in the Hilbert lattices.