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Abstract and Applied Analysis
Volume 2013, Article ID 329451, 4 pages
http://dx.doi.org/10.1155/2013/329451
Research Article

A Best Proximity Point Result in Modular Spaces with the Fatou Property

1Department of Mathematics, King Saud University, Riyadh, Saudi Arabia
2Department of Mathematics, Atilim University, Incek, 06836 Ankara, Turkey

Received 15 June 2013; Accepted 9 September 2013

Academic Editor: Salvador Hernandez

Copyright © 2013 Mohamed Jleli 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

Consider a nonself-mapping , where is a pair of nonempty subsets of a modular space . A best proximity point of is a point satisfying the condition: . In this paper, we introduce the class of proximal quasicontraction nonself-mappings in modular spaces with the Fatou property. For such mappings, we provide sufficient conditions assuring the existence and uniqueness of best proximity points.