Open AccessGeneralized Homogeneity of Means
Author(s) -
Małgorzata Pałys,
Maciej Sablik
Publication year - 2011
Publication title -
isrn mathematical analysis
Language(s) - English
Resource type - Journals
eISSN - 2090-4665
pISSN - 2090-4657
DOI - 10.5402/2011/202409
Subject(s) - homogeneity (statistics) , mathematics , arithmetic , statistics
We extend the classical notions of translativity and homogeneity of means to -homogeneity, that is, invariance with respect to an operation ∶×→. We find the shape of for the arithmetic weighted mean and then the general form of for quasi-linear means. Also, we are interested in characterizations of means. It turns out that no quasi-arithmetic mean can be characterized by -homogeneity with respect to a single operation , one needs to take two of such operations in order to characterize a mean.
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