Abstract and Applied Analysis
Volume 2013 (2013), Article ID 349305, 6 pages
http://dx.doi.org/10.1155/2013/349305
Research Article

On Fixed Point Theory of Monotone Mappings with Respect to a Partial Order Introduced by a Vector Functional in Cone Metric Spaces

Zhilong Li1 and Shujun Jiang2

1School of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China
2Department of Mathematics, Jiangxi University of Finance and Economics, Nanchang 330013, China

Received 19 November 2012; Revised 11 January 2013; Accepted 23 January 2013

Academic Editor: Micah Osilike

Copyright © 2013 Zhilong Li and Shujun Jiang. 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 presented some maximal and minimal fixed point theorems of set-valued monotone mappings with respect to a partial order introduced by a vector functional in cone metric spaces. In addition, we proved not only the existence of maximal and minimal fixed points but also the existence of the largest and the least fixed points of single-valued increasing mappings. It is worth mentioning that the results on single-valued mappings in this paper are still new even in the case of metric spaces and hence they indeed improve the recent results.