Strongly barycentrically associative and preassociative functions
arXiv:1411.5897 · doi:10.1016/j.jmaa.2015.12.046
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.
arXiv admin note: text overlap with arXiv:1406.4345