Set-valued orthogonal additivity
type: Item
instance of: scholarly article
title: Set-valued orthogonal additivity
zbMATH Open document ID: 1328.39039
author: Justyna Sikorska
published in: Set-Valued and Variational Analysis
publication date: 2015-09-02T00:00:00Z
review text: The author gives a form of solutions of the conditional Cauchy functional equation \[ F(x+y)=F(x)+F(y),\qquad x,y\in X,\; x\perp y, \] in the class of set-valued functions \(F:X\to cc(Y)\), where \((X, \perp )\) is an orthogonality space, \(Y\) is a Fréchet space and \(cc(Y)\) denotes the collection of all nonempty compact and convex subsets of \(Y\). Under some weaker assumptions on \(Y\) and the values of \(F\), she also studies the existence of appropriate selections of these solutions.
reviewed by: Krzysztof Ciepliński
Mathematics Subject Classification ID: 39B55
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54C65
zbMATH DE Number: 6477754
zbMATH Keywords: conditional Cauchy functional equation
zbMATH Keywords: set-valued function
zbMATH Keywords: selection
zbMATH Keywords: Fréchet space
MaRDI profile type: Publication
full work available at URL: s11228-015-0321-z
OpenAlex ID: W2157807293
Wikidata QID: Q59408352
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DOI: 10.1007/S11228-015-0321-Z
description: scientific article; zbMATH DE number 6477754