Generalized homogeneity of means
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.
scientific article; zbMATH DE number 5905114