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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 713252, 10 pages
http://dx.doi.org/10.1155/2013/713252
Research Article

Best Proximity Points for Some Classes of Proximal Contractions

1Department of Mathematics, King Abdulaziz University, Science Faculty for Girls, P.O. Box 4087, Jeddah 21491, Saudi Arabia
2Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21859, Saudi Arabia
3DEIM, Università Degli Studi di Palermo, Viale Delle Scienze, 90128 Palermo, Italy

Received 9 May 2013; Revised 11 August 2013; Accepted 11 August 2013

Academic Editor: E. Karapinar

Copyright © 2013 Maryam A. Alghamdi 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

Given a self-mapping and a non-self-mapping , the aim of this work is to provide sufficient conditions for the existence of a unique point , called g-best proximity point, which satisfies . In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function , thereby getting an optimal approximate solution to the equation . An iterative algorithm is also presented to compute a solution of such problems. Our results generalize a result due to Rhoades (2001) and hence such results provide an extension of Banach's contraction principle to the case of non-self-mappings.