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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 672069, 8 pages
http://dx.doi.org/10.1155/2013/672069
Research Article

One-Local Retract and Common Fixed Point in Modular Metric Spaces

Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 8 July 2013; Accepted 19 August 2013

Academic Editor: Mohamed A. Khamsi

Copyright © 2013 Afrah A. N. Abdou. 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

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces, were recently introduced. In this paper we introduced and study the concept of one-local retract in modular metric space. In particular, we investigate the existence of common fixed points of modular nonexpansive mappings defined on nonempty -closed -bounded subset of modular metric space.