Generalized homogeneity of means
type: Item
instance of: scholarly article
title: Generalized homogeneity of means
zbMATH Open document ID: 1217.26068
DOI: 10.5402/2011/202409
author: Małgorzata Pałys
author: Maciej Sablik
published in: ISRN Mathematical Analysis
publication date: 2011-06-08T00:00:00Z
review text: Summary: We extend the classical notions of translativity and homogeneity of means to \(F\)-homogeneity, that is, invariance with respect to an operation \(F \times I \rightarrow I\). We find the shape of \(F\) for the arithmetic weighted mean and then the general form of \(F\) for quasi-linear means. Also, we are interested in characterizations of means. It turns out that no quasi-arithmetic mean can be characterized by \(F\)-homogeneity with respect to a single operation \(F\), one needs to take two of such operations in order to characterize a mean.
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 5905114
MaRDI profile type: Publication
Wikidata QID: Q58689066
full work available at URL: https://doi.org/10.5402/2011/202409
OpenAlex ID: W2061013495
cites work: Q3992445
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description: scientific article; zbMATH DE number 5905114