Results on comparison and sub/super-stabilizability of some new means

TL;DR

This paper analyzes new means introduced by Raïssouli and Rezgui, establishing comparison relations and asymptotic expansions to determine optimal parameters for sub/super-stabilizability within power means.

Contribution

It provides the first comprehensive comparison and asymptotic analysis of these new means, including criteria for sub/super-stabilizability and optimal parameter determination.

Findings

Established comparison relations among new and classical means.

Derived complete asymptotic expansions of mean-maps.

Identified optimal parameters for sub/super-stabilizability.

Abstract

We present analysis of some new means recently introduced by M. Ra\"{i}ssouli and A. Rezgui. We establish comparison relations and results on $(K,N)$-sub/super-stabilizability where $K$ and $N$ belong to the class of power means, denoted by $B_p$, and $M$ is one of the classical or recently studied new means. Assuming that means $K$, $M$ and $N$ have asymptotic expansions, we present the complete asymptotic expansion of the resultant mean-map. As an application of the obtained asymptotic expansions and the asymptotic inequality between $M$ and $\mathcal{R}(B_p,M,B_q)$, we show how to find the optimal parameters $p$ and $q$ for which $M$ is $(B_p,B_q)$-sub/super-stabilizable.