Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 723203, 8 pages
doi:10.1155/2009/723203
An order on subsets of cone metric spaces and fixed points of set-valued contractions
M. Asadi1
, H. Soleimani1
and S.M. Vaezpour3
1Department of Mathematics, Science and Research Branch, Islamic Azad University (IAU), 14778 93855 Tehran, Iran
3Department of Mathematics, Amirkabir University of Technology, 15916 34311 Tehran, Iran
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.