On homogeneous quasideviation means
type: Item
instance of: scholarly article
title: On homogeneous quasideviation means
zbMATH Open document ID: 0664.39005
DOI: 10.1007/BF01836086
author: Zsolt Páles
published in: Aequationes Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137279
review text: The author [Acta Math. Acad. Sci. Hung. 40, 243-260 (1982; Zbl 0541.26006)] has generalized the concept of quasiarithmetic means with weight function introducing the concept of a quasideviation E on an interval I and the quasideviation mean \({\mathfrak M}_ E\). A function E: \(I\times I\to {\mathbb{R}}\) is called a quasideviation on \(I\subset R_+\) if \(sgn E(x,y)=sgn(x-y),\) for \(x,y\in I\), \(y\to E(x,y)\) is continuous in I for each \(x\in I\) and \(y\to E(x,y)/E(x',y)\) is strictly decreasng on (x,x') for \(x<x'\) in I. If \(x_ 1,...,x_ n\in I\), then the equation \(E(x_ 1,y)+...+E(x_ n,y)=0\) has a unique solution \(y=y_ 0\) which is between \(\min_{1\leq i\leq n}x_ i\) and \(\max_{1\leq i\leq n}x_ i\). This value is denoted by \({\mathfrak M}_ E(x_ 1,...,x_ n)\). In the paper the author describes the structure of quasideviations E that generate homogeneous means \({\mathfrak M}_ E\), i.e. such that \({\mathfrak M}_ E(tx_ 1,...,tx_ n)=t{\mathfrak M}_ E(x_ 1,...,x_ n)\) for all \(n\in {\mathbb{N}}\), \(x_ 1,...,x_ n\in I\) with \(tx_ 1,...,tx_ n\in I\).
Mathematics Subject Classification ID: 39B99
Mathematics Subject Classification ID: 26D20
zbMATH DE Number: 4086214
zbMATH Keywords: quasiarithmetic means
reviewed by: Marek Cezary Zdun
MaRDI profile type: Publication
cites work: Q3252924
cites work: Q5804302
cites work: Characterization of quasideviation means
cites work: On the characterization of quasiarithmetic means with weight function
cites work: General inequalities for quasideviation means
description: scientific article; zbMATH DE number 4086214