A dichotomy result for strictly increasing bisymmetric maps
Classical Analysis and ODEs
2022-08-16 v1
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.
Cite
@article{arxiv.2208.07083,
title = {A dichotomy result for strictly increasing bisymmetric maps},
author = {Pál Burai and Gergely Kiss and Patricia Szokol},
journal= {arXiv preprint arXiv:2208.07083},
year = {2022}
}
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12 pages