Abstract and Applied Analysis

Best Proximity Point Theorem in Quasi-Pseudometric Spaces

Robert Plebaniak

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Abstract

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 $\mathrm{inf}\{d(x,y):y\in T(x)\}$, and hence the existence of a consummate approximate solution to the equation $T(X)=x$.

Article information

Source
Abstr. Appl. Anal. Volume 2016 (2016), Article ID 9784592, 8 pages.

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

Permanent link to this document
http://projecteuclid.org/euclid.aaa/1455115147

Digital Object Identifier
doi:10.1155/2016/9784592

Mathematical Reviews number (MathSciNet)
MR3457395

Citation

Plebaniak, Robert. Best Proximity Point Theorem in Quasi-Pseudometric Spaces. Abstr. Appl. Anal. 2016 (2016), Article ID 9784592, 8 pages. doi:10.1155/2016/9784592. http://projecteuclid.org/euclid.aaa/1455115147.


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