Means, generalized harmony proportion and applications
Volume 160 / 2020
Colloquium Mathematicum 160 (2020), 109-118
MSC: 26A17, 26E60, 39B22.
DOI: 10.4064/cm7782-2-2019
Published online: 10 January 2020
Abstract
The classical harmony proportion involving the bivariate arithmetic, harmonic and geometric means $A,H,G$, written in the form $G\circ (A,H)=G,\ $as well as its consequence concerning the convergence of the iterates of the mean-type mapping $(A,H)$ to the mean-type map $(G,G),$ are extended to the case of multivariate means. Applications to some functional equations are presented.
