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2013 Best Proximity Point Results for Modified α - ψ -Proximal Rational Contractions
N. Hussain, M. A. Kutbi, P. Salimi
Abstr. Appl. Anal. 2013(SI43): 1-14 (2013). DOI: 10.1155/2013/927457

Abstract

We first introduce certain new concepts of α - η -proximal admissible and α - η - ψ -rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banach's contraction principle and some of its generalizations as special cases. Moreover, some examples are given to illustrate the usability of the obtained results.

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N. Hussain. M. A. Kutbi. P. Salimi. "Best Proximity Point Results for Modified α - ψ -Proximal Rational Contractions." Abstr. Appl. Anal. 2013 (SI43) 1 - 14, 2013. https://doi.org/10.1155/2013/927457

Information

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

zbMATH: 07095498
MathSciNet: MR3090293
Digital Object Identifier: 10.1155/2013/927457

Rights: Copyright © 2013 Hindawi

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Vol.2013 • No. SI43 • 2013
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