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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 303484, 5 pages
http://dx.doi.org/10.1155/2014/303484
Research Article

Caristi Fixed Point Theorem in Metric Spaces with a Graph

1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
2Department of Mathematical Science, The University of Texas at El Paso, El Paso, TX 79968, USA

Received 27 January 2014; Accepted 11 February 2014; Published 13 March 2014

Academic Editor: Qamrul Hasan Ansari

Copyright © 2014 M. R. Alfuraidan and M. A. Khamsi. 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 discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.