Characterization of generalized quasi-arithmetic means

Matkowski, Janusz and Páles, Zsolt (2015) Characterization of generalized quasi-arithmetic means. ACTA SCIENTIARUM MATHEMATICARUM (SZEGED), 81 (3-4). pp. 447-456. ISSN 0001-6969

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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 → 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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