Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 981517, 8 pages
http://dx.doi.org/10.1155/2012/981517
Research Article

A Fixed Point Theorem for Contraction Type Maps in Partially Ordered Metric Spaces and Application to Ordinary Differential Equations

M. Eshaghi Gordji,1 H. Baghani,1 and G. H. Kim2

1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Department of Mathematics, Kangnam University, Gyeonggi, Yongin 446-702, Republic of Korea

Received 21 November 2011; Accepted 20 December 2011

Academic Editor: Mingshu Peng

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

We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.