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Means, generalized harmony proportion and applications

Volume 160 / 2020

Janusz Matkowski 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.

Authors

  • Janusz MatkowskiFaculty of Mathematics, Computer Science and Econometrics
    University of Zielona Góra
    Szafrana 4a
    65-516 Zielona Góra, Poland
    e-mail

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