Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 905605, 12 pages
doi:10.1155/2009/905605
Research Article

Some Maximal Elements' Theorems in FC-Spaces

Rong-Hua He1,2 and Yong Zhang1

1Department of Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan 610103, China
2Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

Received 30 March 2009; Accepted 1 September 2009

Academic Editor: Nikolaos Papageorgiou

Copyright © 2009 Rong-Hua He and Yong Zhang. 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

Let I be a finite or infinite index set, let X be a topological space, and let (Yi,φNi)i∈I be a family of FC-spaces. For each i∈I, let Ai:X→2Yi be a set-valued mapping. Some new existence theorems of maximal elements for a set-valued mapping and a family of set-valued mappings involving a better admissible set-valued mapping are established under noncompact setting of FC-spaces. Our results improve and generalize some recent results.