Semigroup-valued solutions of the Gołąb-Schinzel type functional equation
type: Item
instance of: scholarly article
title: Semigroup-valued solutions of the Gołąb-Schinzel type functional equation
zbMATH Open document ID: 1124.39021
DOI: 10.1007/BF02960858
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2007-08-29T00:00:00Z
review text: Let \(f\) be a function from the real line \(R\) into a semigrup \((S,0)\) and let \(g\) be a continuous mapping from \(\mathbb R\) into \(\mathbb R\). The author solves completely the functional equation \[ f(x+g(x)y) = f(x) \circ f(y) \] which generalizes the Gołąb-Schinzel equation \[ f\left( x + f(x)^k y \right) = t f(x) f(y), \] where \( t \neq 0\) is a real number and \(k\) is a positive integer. In doing this several previous results are extended.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 5184531
zbMATH Keywords: Gołąb-Schinzel functional equation
zbMATH Keywords: semigroup-valued solutions
author: Jacek Chudziak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5184531