Best proximity point theorem in quasi-pseudometric spaces
type: Item
instance of: scholarly article
title: Best proximity point theorem in quasi-pseudometric spaces
zbMATH Open document ID: 1470.54103
DOI: 10.1155/2016/9784592
published in: Abstract and Applied Analysis
publication date: 2018-08-30T00:00:00Z
review text: Summary: 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 \(\inf \{d(x, y) : y \in T(x) \}\), and hence the existence of a consummate approximate solution to the equation \(T(X) = x\).
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 6929400
Wikidata QID: Q59121565
author: Robert Plebaniak
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/9784592
OpenAlex ID: W2293745487
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description: scientific article; zbMATH DE number 6929400