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arXiv · 2208.07083

A dichotomy result for strictly increasing bisymmetric maps

Pál Burai·Gergely Kiss·Patricia Szokol
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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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Pál Burai, Gergely Kiss, Patricia Szokol. 2022-08-15. A dichotomy result for strictly increasing bisymmetric maps. https://arxiv.org/abs/2208.07083

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