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arXiv · 1501.02857

Characterization of generalized quasi-arithmetic means

Janusz Matkowski·Zsolt Páles
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Abstract

In this paper we characterize generalized quasi-arithmetic means, that is means of the form $M(x_1,...,x_n):=(f_1+...+f_n)^{-1}(f_1(x_1)+...+f_n(x_n))$, where $f_1,...,f_n:I\to\mathbb{R}$ are strictly increasing and continuous functions. Our characterization involves the Gauss composition of the cyclic mean-type mapping induced by $M$ and a generalized bisymmetry equation.

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Janusz Matkowski, Zsolt Páles. 2015-01-13. Characterization of generalized quasi-arithmetic means. https://doi.org/10.14232/actasm-015-028-7

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