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arXiv · 2107.07391

Characterization of quasi-arithmetic means without regularity condition

Pál Burai·Gergely Kiss·Patricia Szokol
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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 $F:I^2\to I$ is continuous. As a consequence, we obtain a finer characterization of quasi-arithmetic means than the classical results of Acz\'el, Kolmogoroff, Nagumo and de Finetti.

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Pál Burai, Gergely Kiss, Patricia Szokol. 2021-07-15. Characterization of quasi-arithmetic means without regularity condition. https://arxiv.org/abs/2107.07391

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