Generalized Homogeneity of Means

الملخص EN

We extend the classical notions of translativity and homogeneity of means to F-homogeneity, that is, invariance with respect to an operation F:I×I→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.