Characterization of the equality of Cauchy means to quasiarithmetic means
arXiv:1907.09186 · doi:10.1016/j.jmaa.2019.123700
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.