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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 181598, 6 pages
http://dx.doi.org/10.1155/2014/181598
Research Article

Best Proximity Point for - -Proximal Contractive Multimaps

1Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology H-12, Islamabad 44000, Pakistan
2Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 27 April 2014; Accepted 21 June 2014; Published 24 July 2014

Academic Editor: Poom Kumam

Copyright © 2014 Muhammad Usman Ali 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

We extend the notions of - -proximal contraction and -proximal admissibility to multivalued maps and then using these notions we obtain some best proximity point theorems for multivalued mappings. Our results extend some recent results by Jleli and those contained therein. Some examples are constructed to show the generality of our results.