A functional equation of Abel revisited
type: Item
instance of: scholarly article
title: A functional equation of Abel revisited
zbMATH Open document ID: 0811.39001
DOI: 10.1007/BF02940785
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1995-05-01T00:00:00Z
review text: The equation \(g(x) + g(y) = h(xf(y) + yf(x))\) \((f,g,h\) unknown) was solved by \textit{N. H. Abel} [J. Reine Angew. Math. 21, 386-394 (1827)] under differentiability suppositions. It also belonged to those functional equations which D. Hilbert in 1900, in the second part of the fifth of his famous unsolved problems, proposed for solution under weaker conditions. The author [Aequationes Math. 39, No. 1, 19-39 (1990; Zbl 0694.39004)] determined the continuous solutions on real intervals containing 0. In the present paper the continuous solutions are offered on intervals not containing 0 but with (real) codomain containing 0. Some further reduction of assumptions is also mentioned.
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 706673
zbMATH Keywords: domain
zbMATH Keywords: Abel functional equation
zbMATH Keywords: differentiable solution
zbMATH Keywords: measurable solution
zbMATH Keywords: locally bounded solution
zbMATH Keywords: continuous solutions
zbMATH Keywords: codomain
author: Maciej Sablik
MaRDI profile type: Publication
cites work: The continuous solution of a functional equation of Abel
full work available at URL: https://doi.org/10.1007/bf02940785
OpenAlex ID: W2058105860
description: scientific article; zbMATH DE number 706673