Characterization of quasi-arithmetic means without regularity condition

2021/07/15 by Burai, Pál, Kiss, Gergely, Szokol, Patricia
#26B99 #26E60 #39B05 #39B22 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.07391

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:I²→ I is continuous. As a consequence, we obtain a finer characterization of quasi-arithmetic means than the classical results of Aczél, Kolmogoroff, Nagumo and de Finetti.

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