Strongly barycentrically associative and preassociative functions

TL;DR

This paper explores advanced properties of functions with indefinite arities, introducing strong barycentric associativity and preassociativity, and generalizing classical mean characterizations to these new concepts.

Contribution

It defines and analyzes strong barycentric associativity and preassociativity, extending the theoretical framework of mean functions and their properties.

Findings

Introduces strong barycentric associativity and preassociativity.

Provides a generalization of Kolmogoroff-Nagumo's mean characterization.

Establishes theoretical foundations for functions with indefinite arities.

Abstract

We study the property of strong barycentric associativity, a stronger version of barycentric associativity for functions with indefinite arities. We introduce and discuss the more general property of strong barycentric preassociativity, a generalization of strong barycentric associativity which does not involve any composition of functions. We also provide a generalization of Kolmogoroff-Nagumo's characterization of the quasi-arithmetic mean functions to strongly barycentrically preassociative functions.