Determination of Means by Invariance

Authors

Jun Ji, Kennesaw State UniversityFollow
Charles Kicey, Valdosta State University

Department

Mathematics

Document Type

Article

Publication Date

10-1-2006

Abstract

If M is a mean on and M(f(x₁),f(x₂),…,f(x_n))=f(M(x₁,x₂,…,x_n)) then we say that M is invariant under f. The problem is to find a class of functions that by invariance determines a mean uniquely. We focus on the geometric mean, which can be transformed to obtain results for other means.