Remarks on solutions to a generalization of the radical functional equations
type: Item
instance of: scholarly article
title: Remarks on solutions to a generalization of the radical functional equations
zbMATH Open document ID: 1397.39016
author: Jens Schwaiger
author: Janusz Brzdȩk
published in: Aequationes Mathematicae
publication date: 2018-09-26T00:00:00Z
review text: During the \(16\)th ``International Conference on Functional Equations and Inequalities'' a talk was given concerning the stability of the so-called radical functional equation, that is, \[ f (\sqrt{x^{2} + y^{2}}) = f (x) + f (y). \] The second author's question about the general solution of the equation itself was answered later by the first one. Contrary to some assertions in the literature the general solution is not an arbitrary quadratic function, but rather an arbitrary function of the form \[ x\longmapsto a(x^{2}), \] with an appropriate additive function \(a\). This paper contains interesting generalizations and applications of the above result.
reviewed by: Eszter Gselmann
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 6944069
zbMATH Keywords: radical functional equation
zbMATH Keywords: groupoid
zbMATH Keywords: semigroup
zbMATH Keywords: Cauchy equation
MaRDI profile type: Publication
full work available at URL: s00010-018-0566-3
OpenAlex ID: W2808329633
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Wikidata QID: Q129673250
DOI: 10.1007/S00010-018-0566-3
description: scientific article; zbMATH DE number 6944069