Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 968271, 13 pages
doi:10.1155/2010/968271
Research Article

Existence of Solutions for η-Generalized Vector Variational-Like Inequalities

Xi Li,1 Jong Kyu Kim,2 and Nan-Jing Huang1,3

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2Department of Mathematics, Kyungnam University, Masan, Kyungnam 631-701, South Korea
3Science & Technology Finance and Mathematical Finance Key Laboratory of Sichuan Province, Sichuan University, Sichuan 610064, China

Received 22 October 2009; Accepted 9 December 2009

Academic Editor: Yeol Je Cho

Copyright © 2010 Xi Li 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

We introduce and study a class of η-generalized vector variational-like inequalities and a class of η-generalized strong vector variational-like inequalities in the setting of Hausdorff topological vector spaces. An equivalence result concerned with two classes of η-generalized vector variational-like inequalities is proved under suitable conditions. By using FKKM theorem, some new existence results of solutions for the η-generalized vector variational-like inequalities and η-generalized strong vector variational-like inequalities are obtained under some suitable conditions.