Abstract and Applied Analysis
Volume 2008 (2008), Article ID 968478, 8 pages
Existence Results for Generalized Vector Equilibrium Problems with Multivalued Mappings via KKM Theory
1Department of Mathematics, School of Science, Razi University, P.O. Box 67149-67346, Kermanshah, Iran
2Center for Research in Mathematics and Physics, School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
3Department of Mathematics, Faculty of Basic Sciences, University of Shahrekord, P.O. Box 88186-34141, Shahrekord, Iran
4Department of Mathematics, College of Arts, Social Sciences, & Celtic Studies, National University of Ireland, Galway, Ireland
Received 6 August 2008; Accepted 21 October 2008
Academic Editor: Paul Eloe
Copyright © 2008 A. P. Farajzadeh 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.
We first define upper sign continuity for a set-valued mapping
and then we consider two types of generalized vector equilibrium problems in topological
vector spaces and provide sufficient conditions under which the solution sets are nonempty
and compact. Finally, we give an application of our main results. The paper generalizes
and improves results obtained by Fang and Huang in (2005).