Equality of two variable weighted means: Reduction to differential equations
type: Item
instance of: scholarly article
title: Equality of two variable weighted means: Reduction to differential equations
zbMATH Open document ID: 0939.39015
author: László Losonczi
published in: Aequationes Mathematicae
publication date: 2000-07-02T00:00:00Z
review text: In this remarkable paper, the author considers the functional equation in a real interval \[ \Phi^{-1} \left( {\Phi (x) F(x) + \Phi (y) F(y)} \over {F(x)+ F(y) } \right) = \Psi^{-1} \left( {\Psi (x) G (x)+ \Psi (y) G(y)} \over {G(x)+G(y) } \right) \tag{*} \] of the equality of two quasiarithmetic means weighted by some weightfuctions \(F\) and \(G\). He shows that if the functions involved are six times differentiable then one can reduce the study of (*) to that of a sixth order differential equation for \( \Phi \circ \Psi^{-1}\), obtaining 32 new families of solutions.
reviewed by: Claudi Alsina
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 1383751
zbMATH Keywords: reduction to differential equations
zbMATH Keywords: weighted means
zbMATH Keywords: functional equation
zbMATH Keywords: quasiarithmetic means
zbMATH Keywords: families of solutions
MaRDI profile type: Publication
full work available at URL: s000100050110
OpenAlex ID: W2040140375
DOI: 10.1007/S000100050110
description: scientific article; zbMATH DE number 1383751