International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 20, Pages 3247-3259
doi:10.1155/IJMMS.2005.3247
Some fixed point theorems for multivalued maps in ordered Banach spaces and applications
Department of Mathematics, Shanxi University, Shanxi, Taiyuan 030006, China
Received 10 November 2004; Revised 10 July 2005
Copyright © 2005 Zhai Chengbo and Yang Chen. 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
The existence of maximal and minimal fixed points for various set-valued operators is discussed. This paper presents some new fixed point theorems in ordered Banach spaces. A necessary and sufficient condition for the existence of the fixed point to a class of multivalued maps has been obtained. The uniqueness of the positive fixed point has been discussed. The results extend and improve the corresponding results. As an application, we utilize the results to study the existence and uniqueness of positive fixed points for a class of convex operators. In the end, we give a simple application to certain integral equations.