Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 967515, 13 pages
doi:10.1155/2011/967515
Research Article

Existence Result of Generalized Vector Quasiequilibrium Problems in Locally 𝐺 -Convex Spaces

Somyot Plubtieng and Kanokwan Sitthithakerngkiet

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 30 November 2010; Accepted 18 February 2011

Academic Editor: Yeol J. Cho

Copyright © 2011 Somyot Plubtieng and Kanokwan Sitthithakerngkiet. 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 deals with the generalized strong vector quasiequilibrium problems without convexity in locally 𝐺 -convex spaces. Using the Kakutani-Fan-Glicksberg fixed point theorem for upper semicontinuous set-valued mapping with nonempty closed acyclic values, the existence theorems for them are established. Moreover, we also discuss the closedness of strong solution set for the generalized strong vector quasiequilibrium problems.