Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 150363, 20 pages
http://dx.doi.org/10.1155/2012/150363
Research Article

Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications

M. Eshaghi Gordji,1 Y. J. Cho,2 S. Ghods,3 M. Ghods,4 and M. Hadian Dehkordi4

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
3Department of Mathematics, Islamic Azad University, Semnan Branch, Semnan, Iran
4Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

Received 30 September 2011; Revised 20 December 2011; Accepted 24 December 2011

Academic Editor: Stefano Lenci

Copyright © 2012 M. Eshaghi Gordji 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

Bhaskar and Lakshmikantham (2006) showed the existence of coupled coincidence points of a mapping 𝐹 from 𝑋 × 𝑋 into 𝑋 and a mapping 𝑔 from 𝑋 into 𝑋 with some applications. The aim of this paper is to extend the results of Bhaskar and Lakshmikantham and improve the recent fixed-point theorems due to Bessem Samet (2010). Indeed, we introduce the definition of generalized 𝑔 -Meir-Keeler type contractions and prove some coupled fixed point theorems under a generalized 𝑔 -Meir-Keeler-contractive condition. Also, some applications of the main results in this paper are given.