On an equation involving weighted quasi-arithmetic means
type: Item
instance of: scholarly article
title: On an equation involving weighted quasi-arithmetic means
zbMATH Open document ID: 1240.26068
published in: Acta Mathematica Hungarica
publication date: 2011-02-25T00:00:00Z
review text: The main theorem of this paper gives a full solution of the Matkowski-Sutô type functional equation \[ \kappa x+(1-\kappa)y=\lambda \varphi^{-1}(\mu\varphi(x)+(1-\mu)\varphi(y)) +(1-\lambda)\psi^{-1}(\nu\psi(x)+(1-\nu)\psi(y)). \] The unknown functions \(\varphi\) and \(\psi\) are assumed to be continuous and strictly monotone on an interval (these are natural regularity conditions), \(\kappa,\lambda\) are real numbers different from zero and one, \(\mu,\nu\in]0,1[\) are weights.
reviewed by: Pál Burai
Mathematics Subject Classification ID: 26E60
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 5857785
zbMATH Keywords: functional equation
zbMATH Keywords: quasi-arithmetic mean
zbMATH Keywords: invariant mean
zbMATH Keywords: regularity of solutions
author: Justyna Jarczyk
MaRDI profile type: Publication
full work available at URL: s10474-010-9246-z
OpenAlex ID: W2014838786
cites work: Mean values and functional equations
cites work: Q3653789
cites work: On linear combinations of weighted quasi-arithmetic means
cites work: On two-variable means with variable weights
cites work: Q4793074
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cites work: Q3653888
cites work: Invariance in the class of weighted quasi-arithmetic means
cites work: Invariant and complementary quasi-arithmetic means
DOI: 10.1007/S10474-010-9246-Z
description: scientific article; zbMATH DE number 5857785