Characterization of generalized quasi-arithmetic means

Janusz Matkowski, Zsolt Páles

Published 2015-01-13Version 1

In this paper we characterize generalized quasi-arithmetic means, that is means of the form $M(x_1,\dots,x_n):=(f_1+\cdots+f_n)^{-1}(f_1(x_1)+\cdots+f_n(x_n))$, where $f_1,\dots,f_n:I\to\mathbb{R}$ 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.