Characterization of generalized quasi-arithmetic means
Abstract
In this paper we characterize generalized quasi-arithmetic means, that is means of the form M(x1,...,xn):=(f1+...+fn)-1(f1(x1)+...+fn(xn)), where f1,...,fn:I 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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