Characterization of quasi-arithmetic means without regularity condition

Burai, Pál József and Kiss, Gergely and Szokol, Patrícia Ágnes (2021) Characterization of quasi-arithmetic means without regularity condition. ACTA MATHEMATICA HUNGARICA. ISSN 0236-5294

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Abstract

In this paper we show that bisymmetry, which is an algebraic property, has a regularity improving feature. More precisely, we prove that every bisymmetric, partially strictly monotonic, reflexive and symmetric function F : I 2 → I is continuous. As a consequence, we obtain a finer characterization of quasiarithmetic means than the classical results of Acz´el

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