On controlled extensions of functions.
type: Item
instance of: scholarly article
title: On controlled extensions of functions.
zbMATH Open document ID: 1034.54012
DOI: 10.1016/S0022-247X(03)00292-0
author: Jože Malešič
author: Pavel V. Semenov
author: Dušan Repovš
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-09-25T00:00:00Z
review text: The aim of the present paper is to offer conditions for resolving the controlled extension problem for a closed subset \(A\) of a normal space \(X\) given any numerical functions \(E: \mathbb{R}^2\to \mathbb{R}\). More precisely, if the functions \(f: A\to \mathbb{R}\), \(g: A\to \mathbb{R}\) and \(h: X\to\mathbb{R}\) satisfy the equality \(E(f(a),g(a))= h(a)\), for every \(a\in A\), then the authors are interested in finding the extensions \(\widehat f\) and \(\widehat g\) of \(f\) and \(g\), respectively, such that \(E(\widehat f(x),\widehat g(x))= h(x)\), for every \(x\in X\). They also give interesting generalizations of earlier results concerning \(E(u,v)= u\cdot v\) by using the techniques of selections of paraconvex-valued LSC mappings and soft single-valued mappings.
Mathematics Subject Classification ID: 54C20
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 54C30
zbMATH DE Number: 1985888
zbMATH Keywords: Multivalued mapping
zbMATH Keywords: Continuous selection
zbMATH Keywords: Controlled extension
zbMATH Keywords: Normal space
zbMATH Keywords: Soft mapping
reviewed by: Chariklia Konstadilaki
MaRDI profile type: Publication
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full work available at URL: s0022-247x(03)00292-0
OpenAlex ID: W2071051964
description: scientific article; zbMATH DE number 1985888