Measure of nonhyperconvexity and fixed-point theorems
type: Item
instance of: scholarly article
title: Measure of nonhyperconvexity and fixed-point theorems
zbMATH Open document ID: 1057.47059
DOI: 10.1155/S1085337503205017
author: Dariusz Bugajewski
author: Rafa Espínola
published in: Abstract and Applied Analysis
publication date: 2003-03-17T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.aaa/1050426056
full work available at URL: https://eudml.org/doc/51171
review text: The authors introduce the concept of ``measure \(\mu\) of hyperconvexity of a metric space \(X\)'' in order to generalize the Schauder fixed-point theorem in hyperconvex spaces. Of the various interesting results, we quote only Theorem 3.7. Let \(A\) be a nonempty bounded and complete metric space and let \(f:A\to A\) be continuous and both \(\alpha\)- and \(\mu\)-contractive. Then \(f\) has a fixed point. This paper is well-written and contains most of the terminology it uses.
reviewed by: Carlos R. Borges
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54C55
zbMATH DE Number: 1883741
zbMATH Keywords: fixed point
zbMATH Keywords: hyperconvex
zbMATH Keywords: \(\mu\)-measure
zbMATH Keywords: \(\mu\)-contractive
MaRDI profile type: Publication
OpenAlex ID: W2052342344
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description: scientific article; zbMATH DE number 1883741