Open Access
2013 Best Proximity Points for Some Classes of Proximal Contractions
Maryam A. Alghamdi, Naseer Shahzad, Francesca Vetro
Abstr. Appl. Anal. 2013(SI43): 1-10 (2013). DOI: 10.1155/2013/713252


Given a self-mapping g : A A and a non-self-mapping T : A B , the aim of this work is to provide sufficient conditions for the existence of a unique point x A , called g-best proximity point, which satisfies d g x , T x = d A , B . In so doing, we provide a useful answer for the resolution of the nonlinear programming problem of globally minimizing the real valued function x d g x , T x , thereby getting an optimal approximate solution to the equation T x = g x . 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.


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Maryam A. Alghamdi. Naseer Shahzad. Francesca Vetro. "Best Proximity Points for Some Classes of Proximal Contractions." Abstr. Appl. Anal. 2013 (SI43) 1 - 10, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095261
MathSciNet: MR3108642
Digital Object Identifier: 10.1155/2013/713252

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI43 • 2013
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