Journal of Applied Mathematics
Volume 2012 (2012), Article ID 183040, 12 pages
http://dx.doi.org/10.1155/2012/183040
Research Article

The Convergent Behavior for Parametric Generalized Vector Equilibrium Problems

Yen-Cherng Lin,1 Po-Jen Cheng,2 and Su-Ling Lee3,4

1Department of Occupational Safety and Health, China Medical University, Taichung 404, Taiwan
2Department of Applied Mathematics, National Chiayi University, Chiayi 60004, Taiwan
3Szu Chen Junior High School, Taichung 43441, Taiwan
4Department of Applied Statistics, Chung Hua University, Hsinchu 300, Taiwan

Received 14 September 2012; Accepted 24 October 2012

Academic Editor: Jen Chih Yao

Copyright © 2012 Yen-Cherng Lin 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 study some properties for parametric generalized vector equilibrium problems and the convergent behavior for the correspondent solution sets of this problem under some suitable conditions. Several existence results and the topological structures of the efficient solutions set are established. Some new results of existence for weak solutions and strong solutions are derived. Finally, we give some examples to illustrate our theory including the example studied by Fang (1992), who established the perturbed nonlinear program and described successfully that the optimal solution of will approach the optimal solution of linear program (P).