Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 134897, 11 pages
doi:10.1155/2010/134897
Research Article

Coupled Coincidence Point and Coupled Common Fixed Point Theorems in Partially Ordered Metric Spaces with 𝑤 -Distance

Mujahid Abbas,1 Dejan Ilić,2 and Muhammad Ali Khan1

1Department of Mathematics, Lahore University of Management Sciences, 54792 Lahore, Pakistan
2Department of Mathematics, Faculty of Sciences and Mathematics, University of Niŝ, Viŝegradska 33, 18000 Niŝ, Serbia

Received 7 April 2010; Accepted 18 October 2010

Academic Editor: Hichem Ben-El-Mechaiekh

Copyright © 2010 Mujahid Abbas 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

We introduce the concept of a 𝑤 -compatible mapping to obtain a coupled coincidence point and a coupled point of coincidence for nonlinear contractive mappings in partially ordered metric spaces equipped with 𝑤 -distances. Related coupled common fixed point theorems for such mappings are also proved. Our results generalize, extend, and unify several well-known comparable results in the literature.