Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 761086, 16 pages
doi:10.1155/2009/761086
Research Article
Assad-Kirk-Type Fixed Point Theorems for a Pair of Nonself Mappings on Cone Metric Spaces
1Mathematical Institute SANU, Knez Mihailova 36, 11001 Beograd, Serbia
2Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Serbia
3Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia
4Department of Mathematics, Indiana University, Bloomington, IN 47405-7106, USA
Received 7 February 2009; Accepted 27 April 2009
Academic Editor: William A. Kirk
Copyright © 2009 S. Janković 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
New fixed point results for a pair of non-self mappings defined on a closed subset of a metrically convex cone metric space (which is not necessarily normal) are obtained. By adapting Assad-Kirk's method the existence
of a unique common fixed point for a pair of non-self mappings is proved, using only the assumption that the cone interior is nonempty. Examples show that the obtained results are proper extensions of the existing ones.