On a generalization of u-means

Abstract

In this paper we present an extension of Bauer's work about u-means. We consider a kind of composition of an admissible function u(x) (described by Bauer) and of a compatible function ϕ(x). This construction allows us to define (u,ϕ)-means. When ϕ(x)=x, the (u,ϕ)-means are the u-means introduced by Bauer. The arithmetic, geometric and harmonic means are special cases.