Christensen measurable solutions of some functional equation
type: Item
instance of: scholarly article
title: Christensen measurable solutions of some functional equation
zbMATH Open document ID: 1187.28024
author: Eliza Jabłońska
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-02-05T00:00:00Z
review text: Given a separable \(F\)-space \(X\) over the field \(K\) of reals or complex numbers, the author finds the solutions of the functional equation \[ f(x + M(f(x))y) = f(x) f(y) \] in the class of functions \(M: K \to K\) and Christensen measurable function \(f: X \to K\). This equation generalizes the classical Cauchy's equation for the exponential function (\(M \equiv 1) \) and the Goląb-Schinzel equation (\(M=j_K\)).
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 28E05
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 5666159
zbMATH Keywords: Christensen measurable set
zbMATH Keywords: Gola\"b-Schinzel equation
zbMATH Keywords: exponential function
MaRDI profile type: Publication
full work available at URL: j.na.2009.10.043
OpenAlex ID: W1969443812
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DOI: 10.1016/J.NA.2009.10.043
description: scientific article; zbMATH DE number 5666159