Characterization of generalized quasi-arithmetic means
Copyright policy )Characterization of generalized quasi-arithmetic means
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.
QA Mathematics / matematika, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 39B40, Iteration theory, iterative and composite equations, characterization, Means, generalized quasi-arithmetic mean, bisymmetry
QA Mathematics / matematika, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 39B40, Iteration theory, iterative and composite equations, characterization, Means, generalized quasi-arithmetic mean, bisymmetry
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