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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 897198, 15 pages
http://dx.doi.org/10.1155/2012/897198
Research Article

On Coupled Fixed Point Theorems for Nonlinear Contractions in Partially Ordered -Metric Spaces

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 31 July 2012; Revised 2 October 2012; Accepted 2 October 2012

Academic Editor: Simeon Reich

Copyright © 2012 S. A. Mohiuddine and Abdullah Alotaibi. 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

Two concepts—one of the coupled fixed point and the other of the generalized metric space—play a very active role in recent research on the fixed point theory. The definition of coupled fixed point was introduced by Bhaskar and Lakshmikantham (2006) while the generalized metric space was introduced by Mustafa and Sims (2006). In this work, we determine some coupled fixed point theorems for mixed monotone mapping satisfying nonlinear contraction in the framework of generalized metric space endowed with partial order. We also prove the uniqueness of the coupled fixed point for such mappings in this setup.