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A dichotomy result for strictly increasing bisymmetric maps

2022/08/15 by Pál Burai, Burai, Pál, Gergely Kiss +3
Mathematics · #26B99 #26E60 #39B05 #39B22 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2208.07083

openalex publication_date 2022/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we show some remarkable consequences of the method which proves that every bisymmetric, symmetric, reflexive, strictly monotonic binary map on a proper interval is continuous, in particular it is a quasi-arithmetic mean. Now we demonstrate that this result can be refined in the way that the symmetry condition can be weakened by assuming symmetry only for a pair of distinct points of an interval.

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