Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 936428, 15 pages
doi:10.1155/2011/936428
Research Article

Boundedness and Nonemptiness of Solution Sets for Set-Valued Vector Equilibrium Problems with an Application

Ren-You Zhong,1 Nan-Jing Huang,1 and Yeol Je Cho2

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea

Received 25 October 2010; Accepted 19 January 2011

Academic Editor: K. Teo

Copyright © 2011 Ren-You Zhong 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

This paper is devoted to the characterizations of the boundedness and nonemptiness of solution sets for set-valued vector equilibrium problems in reflexive Banach spaces, when both the mapping and the constraint set are perturbed by different parameters. By using the properties of recession cones, several equivalent characterizations are given for the set-valued vector equilibrium problems to have nonempty and bounded solution sets. As an application, the stability of solution set for the set-valued vector equilibrium problem in a reflexive Banach space is also given. The results presented in this paper generalize and extend some known results in Fan and Zhong (2008), He (2007), and Zhong and Huang (2010).