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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 206515, 9 pages
http://dx.doi.org/10.1155/2013/206515
Research Article

Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction

1Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bang Mod, Bangkok 10140, Thailand
2Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
3Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat 395007, India

Received 10 May 2013; Accepted 9 July 2013

Academic Editor: Salvador Hernandez

Copyright © 2013 Poom Kumam 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

Ran and Reurings (2004) established an interesting analogue of Banach Contraction Principle in a complete metric space equipped with a partial ordering and also utilized the same oneto discuss the existence of solutions to matrix equations. Motivated by this paper, we prove results on coincidence points for a pair of weakly increasing mappings satisfying a nonlinear contraction condition described by a rational expression on an ordered complete metric space. The uniqueness of common fixed point is also discussed. Some examples are furnished to demonstrate the validity of the hypotheses of our results. As an application, we derive an existence theorem for the solution of an integral equation.