Table of Contents
International Journal of Analysis
Volume 2013, Article ID 762380, 7 pages
http://dx.doi.org/10.1155/2013/762380
Research Article

Vector Variational-Like Inequalities with Generalized Semimonotone Mappings

Department of Mathematics, BITS Pilani, Dubai Campus, 345055 Dubai, UAE

Received 14 August 2012; Accepted 20 October 2012

Academic Editor: Ying Hu

Copyright © 2013 Suhel Ahmad Khan. 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 the concepts of generalized relaxed monotonicity and generalized relaxed semimonotonicity. We consider a class of generalized vector variationa-llike inequality problem involving generalized relaxed semimonotone mapping. By using Kakutani-Fan-Glicksberg’s fixed-point theorem, we prove the solvability for this class of vector variational-like inequality with relaxed monotonicity assumptions. The results presented in this paper generalize some known results for vector variational inequality in recent years.