\(q\)-hyperconvexity in quasipseudometric spaces and fixed point theorems
type: Item
instance of: scholarly article
title: \(q\)-hyperconvexity in quasipseudometric spaces and fixed point theorems
zbMATH Open document ID: 1257.54040
DOI: 10.1155/2012/765903
author: Olivier Olela Otafudu
author: Hans Peter Künzi
published in: Journal of Function Spaces and Applications
publication date: 2012-11-07T00:00:00Z
review text: Let \((H,d)\) be a \(q\)-hyperconvex \(T_0\)-quasimetric space, and \({\mathcal E}_q(H)\) stand for the set of all (nonempty) externally \(q\)-hyperconvex subsets of \((H,d)\). The following are the main results in the paper: Theorem 1. Let \(X\) be a nonempty set, and \(T^*:X\to {\mathcal E}_q(H)\) be a mapping. There exists then a mapping \(T:X\to H\) which selects \(T^*\) [i.e.: \(T(x)\in T^*(x)\), for all \(x\in X\)], such that \(d(Tx,Ty)\leq d_H(T^*(x),T^*(y))\), for all \(x,y\in X\). Theorem 2. Let \(T^*:H\to {\mathcal E}_q(H)\) be a nonexpansive map with \(\text{Fix}(T^*)\neq \emptyset\). There exists then a nonexpansive mapping \(T:H\to H\) which selects \(T^*\), such that \(\text{Fix}(T)=\text{Fix}(T^*)\). The obtained facts complete the investigation of these concepts started in \textit{E. Kemajou, H.-P. Künzi} and \textit{O. O. Otafudu} [Topology Appl. 159, No. 9, 2463--2475 (2012; Zbl 1245.54023)].
reviewed by: Mihai Turinici
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54C65
zbMATH DE Number: 6102741
zbMATH Keywords: hyperconvexity
zbMATH Keywords: quasipseudometric space
zbMATH Keywords: fixed point hyperconvexity
zbMATH Keywords: fixed point
Wikidata QID: Q58908390
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/765903
OpenAlex ID: W2061821275
cites work: The Isbell-hull of a di-space
cites work: The ultra-quasi-metrically injective hull of a \(T_0\)-ultra-quasi-metric space
cites work: Q3730636
cites work: Q3966761
cites work: Q5191281
cites work: Completeness in quasi-metric spaces and Ekeland variational principle
cites work: Quasi-metrics and monotone normality
cites work: The complexity probabilistic quasi-metric space
cites work: Domain theoretic characterisations of quasi-metric completeness in terms of formal balls
cites work: On Quasi-Uniformities in Hyperspaces
cites work: Q3123097
cites work: An Introduction to Metric Spaces and Fixed Point Theory
cites work: On nonlinear contraction semigroups in sup norm spaces
cites work: Existence of Fixed Points of Nonexpansive Mappings in Certain Banach Lattices
cites work: Q3799313
cites work: Introduction to hyperconvex spaces
cites work: Fixed point and selection theorems in hyperconvex spaces
cites work: On asymptotically nonexpansive mappings in hyperconvex metric spaces
cites work: Hyperconvexity and approximate fixed points
cites work: Extension of uniformly continuous transformations and hyperconvex metric spaces
Recommended article: Q4583245
Recommended article: \(q^\lambda \)-hyperconvexity in quasi-metric spaces
Recommended article: Fixed point theorems for \((p,q)\)-quasi-contraction mappings in cone metric spaces
Recommended article: Q5079012
Recommended article: Fixed point results in quasi-cone metric spaces
Recommended article: Q3145705
Recommended article: \(Q\)-functions on quasimetric spaces and fixed points for multivalued maps
Recommended article: Q4844858
Recommended article: Q3784844
Recommended article: Fixed-point theorems in hyperconvex spaces revisited
description: scientific article; zbMATH DE number 6102741