Characterization of the equality of Cauchy means to quasiarithmetic means

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 g...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2020-04, Vol.484 (1), p.123700, Article 123700
Main Authors: Lovas, Rezső L., Páles, Zsolt, Zakaria, Amr
Format: Article
Language:English
Subjects:
Cauchy mean
Equality problem
Functional equation
Quasiarithmetic mean
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Summary: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 non-degenerate conic section.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123700