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International Journal of Analysis
Volume 2013, Article ID 917158, 6 pages
http://dx.doi.org/10.1155/2013/917158
Research Article

Remarks on -Metric Spaces

1Department of Mathematics, King Saud University, Saudi Arabia
2Dipartimento di Matematica e Informatica, Università degli Studi di Palermo, Via Archirafi 34, 90123 Palermo, Italy
3DEIM, Università degli Studi di Palermo, 90128 Palermo, Italy

Received 13 September 2012; Revised 5 November 2012; Accepted 5 November 2012

Academic Editor: Serge Nicaise

Copyright © 2013 Bessem Samet 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

In 2005, Mustafa and Sims (2006) introduced and studied a new class of generalized metric spaces, which are called -metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric) -metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.