On the Hardy property of mixed means

TL;DR

This paper investigates the Hardy property of mixed means, exploring the effects of relaxing certain axioms like monotonicity and repetition invariance, and determines the Hardy constant for specific mixed means.

Contribution

It introduces new conditions for Hardy property analysis by weakening axioms and applies these to find Hardy constants for certain mixed means.

Findings

Established Hardy constants for specific mixed means

Showed that monotonicity can be replaced by weaker conditions

Extended previous results by relaxing key axioms

Abstract

Hardy property of means has been extensively studied by P\'ales and Pasteczka since 2016. The core of this research is based on few of their properties: concavity, symmetry, monotonicity, repetition invariance and homogeneity (last axiom was recently omitted using some homogenizations techniques). In the present paper we deliver a study of possible omitting monotonicity and replacing repetition invariance by a weaker axiom. These results are then used to establish the Hardy constant for certain types of mixed means.