Table of Contents
Journal of Operators
Volume 2013, Article ID 404573, 8 pages
http://dx.doi.org/10.1155/2013/404573
Research Article

A Fixed Point Theorem in Orbitally Complete Partially Ordered Metric Spaces

1Department of Mathematics, Andhra University, Visakhapatnam 530 003, India
2Department of Mathematics, Lendi Institute of Engineering and Technology, Vizianagaram 535 005, India
3Department of Mathematics, Jimma University, Jimma-378, Ethiopia

Received 14 June 2013; Revised 30 October 2013; Accepted 2 November 2013

Academic Editor: Ram U. Verma

Copyright © 2013 G. V. R. Babu 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

Let be a partially ordered set and be a mapping. We prove a fixed point theorem for the map satisfying a contractive condition in orbits, when is -orbitally complete. Our result extends and generalizes the results of Samet et al. (2013) to partially ordered sets. Also, we generalize the results of Ran and Reurings (2004).