International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 430930, 10 pages
doi:10.1155/2009/430930
Research Article

On System of Generalized Vector Quasiequilibrium Problems with Applications

Jian-Wen Peng1 and Lun Wan2

1College of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, China
2Scientific Research Office, Chongqing Normal University, Chongqing 400047, China

Received 3 July 2009; Accepted 19 August 2009

Academic Editor: Marco Squassina

Copyright © 2009 Jian-Wen Peng and Lun Wan. 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 a new system of generalized vector quasiequilibrium problems which includes system of vector quasiequilibrium problems, system of vector equilibrium problems, and vector equilibrium problems, and so forth in literature as special cases. We prove the existence of solutions for this system of generalized vector quasi-equilibrium problems. Consequently, we derive some existence results of a solution for the system of generalized quasi-equilibrium problems and the generalized Debreu-type equilibrium problem for both vector-valued functions and scalar-valued functions.