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.
Let be a finite or infinite index set, let be a topological space, and let be a family of
-spaces. For each , let 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 -spaces. Our results
improve and generalize some recent results.