Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 723203, 8 pages
doi:10.1155/2009/723203
Research Article

An Order on Subsets of Cone Metric Spaces and Fixed Points of Set-Valued Contractions

M. Asadi,1 H. Soleimani,1 and S. M. Vaezpour2,3

1Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), 14778 93855 Tehran, Iran
2Department of Mathematics, Amirkabir University of Technology, 15916 34311 Tehran, Iran
3Department of Mathematics, Newcastle University, Newcastle, NSW 2308, Australia

Received 16 April 2009; Revised 19 August 2009; Accepted 22 September 2009

Academic Editor: Marlene Frigon

Copyright © 2009 M. Asadi et al. 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

In this paper at first we introduce a new order on the subsets of cone metric spaces then, using this definition, we simplify the proof of fixed point theorems for contractive set-valued maps, omit the assumption of normality, and obtain some generalization of results.