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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 842515, 17 pages
http://dx.doi.org/10.1155/2012/842515
Research Article

Fixed Points, Maximal Elements and Equilibria of Generalized Games in Abstract Convex Spaces

Department of Mathematics, Tianjin Polytechnic University, Tianjin, Hedong 300387, China

Received 24 October 2012; Accepted 23 November 2012

Academic Editor: Yongfu Su

Copyright © 2012 Yan-Mei Du. 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 firstly prove some new fixed point theorems for set-valued mappings in noncompact abstract convex space. Next, two existence theorems of maximal elements for class of mapping and -majorized mapping are obtained. As in applications, we establish new equilibria existence theorems for qualitative games and generalized games. Our theorems improve and generalize the most known results in recent literature.