Quotient mean, its invariance with respect to a quasi-arithmetic mean-type mapping, and some applications
type: Item
instance of: scholarly article
title: Quotient mean, its invariance with respect to a quasi-arithmetic mean-type mapping, and some applications
zbMATH Open document ID: 1232.26053
author: Janusz Matkowski
published in: Aequationes Mathematicae
publication date: 2012-01-10T00:00:00Z
review text: The author introduces the so-called quotient mean \[ Q_{f,g}(x,y):=\left( \frac{f}{g} \right) ^{-1} \left( \frac{f(x)} {g(y)} \right) \] for functions \(f\) and \(g\) defined on an interval and satisfying certain conditions. The classical arithmetic, geometric and harmonic means are particular cases. The invariance of this mean with respect to the weighted quasi-arithmetic mean is examined. Applications to the iterations of means are pointed out, too.
reviewed by: József Sándor
Mathematics Subject Classification ID: 26E60
Mathematics Subject Classification ID: 39B22
zbMATH DE Number: 5996229
zbMATH Keywords: means
zbMATH Keywords: quotient mean
zbMATH Keywords: invariant mean
zbMATH Keywords: mean-type mapping
zbMATH Keywords: iterations
zbMATH Keywords: functional equation
MaRDI profile type: Publication
full work available at URL: s00010-011-0088-8
OpenAlex ID: W2019080103
cites work: Q3751634
cites work: Q4441514
cites work: Q4793074
cites work: Q4947993
cites work: Invariant and complementary quasi-arithmetic means
cites work: Q5439426
cites work: Q3007316
DOI: 10.1007/S00010-011-0088-8
description: scientific article; zbMATH DE number 5996229