Mean value property and associated functional equations
type: Item
instance of: scholarly article
title: Mean value property and associated functional equations
zbMATH Open document ID: 0931.39013
author: Janusz Matkowski
published in: Aequationes Mathematicae
publication date: 2000-02-22T00:00:00Z
review text: The author offers as main result the solution of the functional equation \[ \frac{g(x)-g(y)}{x-y}=\phi(\frac{f(x)-f(y)}{x-y}). \] If \(f\) is strictly convex (from above or below) then \(\phi\) is affine and \(g(t)\) is a linear combination of \(f(t),t\) and \(1.\) The result is then applied to determine \(g\) and \(h\) in \([g(x)-g(y)]/(x-y)=h[M(x,y)]\) for \(x\neq y\) and for different mean values \(M,\) in particular for the means studied by \textit{K. B. Stolarsky} [Math. Mag. 48, 87-92 (1975; Zbl 0302.26003)].
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 1346972
zbMATH Keywords: functional equations
zbMATH Keywords: convex functions
zbMATH Keywords: mean values
zbMATH Keywords: Stolarsky means
MaRDI profile type: Publication
full work available at URL: s000100050006
OpenAlex ID: W2068592071
DOI: 10.1007/S000100050006
description: scientific article; zbMATH DE number 1346972