Homogeneous Beta-type functions
Martin Himmel, Janusz Matkowski
TL;DR
This paper characterizes all p-homogeneous beta-type functions, showing that the harmonic mean uniquely satisfies the homogeneity property among such functions, and revisits related classical results with new reformulations.
Contribution
It provides a complete classification of p-homogeneous beta-type functions and establishes the harmonic mean as the unique homogeneous mean among them.
Findings
All p-homogeneous beta-type functions are determined.
A beta-type function is a homogeneous mean iff it is the harmonic mean.
Reformulation of Heuvers' result using Cauchy difference and harmonic mean.
Abstract
All beta-type functions, which are p-homogeneous, are determined. Applying this result, we show that a beta-type function is a homogeneous mean iff it is the harmonic one. A reformulation of a result due to Heuvers in terms of a Cauchy difference and the harmonic mean is given.
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Taxonomy
TopicsFunctional Equations Stability Results · Mathematical and Theoretical Analysis · Mathematical functions and polynomials