Open Access
2016 Best Proximity Point Theorem in Quasi-Pseudometric Spaces
Robert Plebaniak
Abstr. Appl. Anal. 2016: 1-8 (2016). DOI: 10.1155/2016/9784592


In quasi-pseudometric spaces (not necessarily sequentially complete), we continue the research on the quasi-generalized pseudodistances. We introduce the concepts of semiquasiclosed map and contraction of Nadler type with respect to generalized pseudodistances. Next, inspired by Abkar and Gabeleh we proved new best proximity point theorem in a quasi-pseudometric space. A best proximity point theorem furnishes sufficient conditions that ascertain the existence of an optimal solution to the problem of globally minimizing the error inf{d(x,y):yT(x)}, and hence the existence of a consummate approximate solution to the equation T(X)=x.


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Robert Plebaniak. "Best Proximity Point Theorem in Quasi-Pseudometric Spaces." Abstr. Appl. Anal. 2016 1 - 8, 2016.


Received: 24 October 2015; Revised: 17 December 2015; Accepted: 20 December 2015; Published: 2016
First available in Project Euclid: 10 February 2016

zbMATH: 06929400
MathSciNet: MR3457395
Digital Object Identifier: 10.1155/2016/9784592

Rights: Copyright © 2016 Hindawi

Vol.2016 • 2016
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