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International Journal of Analysis
Volume 2014, Article ID 586096, 9 pages
http://dx.doi.org/10.1155/2014/586096
Research Article

Coupled Fixed Point Theorems for ()-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications

1Department of Mathematics, Ahir College, Rewari 123401, India
2HAS Department, YMCAUST, Faridabad 121006, India
3Department of Mathematics, DCRUST, Murthal, Sonepat 131039, India

Received 14 November 2013; Accepted 22 January 2014; Published 18 March 2014

Academic Editor: Tohru Ozawa

Copyright © 2014 Manish Jain 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

The object of this paper is to establish the existence and uniqueness of coupled fixed points under a (, )-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012) and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006), and Luong and Thuan (2011). The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.