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Mathematical Problems in Engineering
Volume 2013, Article ID 504609, 7 pages
Research Article

-Metric Space: A Generalization

1Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran
2Department of Mathematics, Atilim University, İncek, 06836 Ankara, Turkey
3Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia

Received 27 May 2013; Accepted 25 July 2013

Academic Editor: Bashir Ahmad

Copyright © 2013 Farshid Khojasteh 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.


We introduce the notion of -metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a -metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.