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arXiv · 1907.09186

Characterization of the equality of Cauchy means to quasiarithmetic means

Rezső L. Lovas·Zsolt Páles·Amr Zakaria
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Abstract

The main result of this paper provides six necessary and sufficient conditions under various regularity assumptions for a so-called Cauchy mean to be identical to a two-variable quasiarithmetic mean. One of these conditions says that a Cauchy mean is quasiarithmetic if and only if the range of its generating functions is covered by a nondegenerate conic section.

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Rezső L. Lovas, Zsolt Páles, Amr Zakaria. 2019-07-22. Characterization of the equality of Cauchy means to quasiarithmetic means. https://doi.org/10.1016/j.jmaa.2019.123700

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