Existence and convergence results for best proximity points in cone metric spaces
type: Item
instance of: scholarly article
title: Existence and convergence results for best proximity points in cone metric spaces
zbMATH Open document ID: 1307.54046
author: Byung-Soo Lee
published in: Numerical Algebra, Control and Optimization
publication date: 2014-12-05T00:00:00Z
review text: This paper is an attempt to extend the best proximity results of \textit{S. S. Basha} [Optim. Lett. 7, No. 6, 1167--1177 (2013; Zbl 1298.90075)] to the framework of cone metric spaces in the sense of \textit{L.-G. Huang} and \textit{X. Zhang} [J. Math. Anal. Appl. 332, No. 2, 1468--1476 (2007; Zbl 1118.54022)]. However, several places remain unclear. E.g., what is the distance \(d(A,B)\) of sets in a cone metric space? What is the norm \(\|S\|\) of an operator in a cone metric space? In Theorem 3.5, what is the connection of \(x^*\) with the constructed sequences \(\{x_n\}\) and \(\{y_n\}\)? Etc. Moreover, only trivial examples are given, with orderings which are total, so the need of considering more general orders is not justified.
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 6376984
zbMATH Keywords: cone metric space
zbMATH Keywords: generalized cone proximal \(\phi\)-cyclic contraction pairs
zbMATH Keywords: normal cone
zbMATH Keywords: best proximity points
zbMATH Keywords: non-self mappings
MaRDI profile type: Publication
full work available at URL: naco.2014.4.133
OpenAlex ID: W2320435126
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DOI: 10.3934/NACO.2014.4.133
description: scientific article; zbMATH DE number 6376984