Abstract. 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\colon I\to{\msbm 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.
DOI: 10.14232/actasm-015-028-7
AMS Subject Classification
(1991): 39B40
Keyword(s):
generalized quasi-arithmetic mean,
bisymmetry,
characterization
Received April 9, 2015, and in revised form June 2, 2015. (Registered under 28/2015.)
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