On the Isomorphic Means and Comparison Inequalities
Abstract
Based on collection of bijections, variable and function are extended into ``isomorphic variable'' and ``dual-variable-isomorphic function'', then mean values such as arithmetic mean and mean of a function are extended to ``isomorphic means''. 7 sub-classes of isomorphic mean of a function are distinguished. Comparison problems of isomorphic means are discussed. A sub-class(class V) of isomorphic mean of a function related to Cauchy mean value is utilized for generation of bivariate means e.g. quasi-Stolarsky means. Demonstrated as an example of math related to ``isomorphic frames'', this paper attempts to unify current common means into a better extended family of means.
Cite
@article{arxiv.2308.06500,
title = {On the Isomorphic Means and Comparison Inequalities},
author = {Yuan Liu},
journal= {arXiv preprint arXiv:2308.06500},
year = {2023}
}
Comments
4 illustrations. Keywords: Isomorphic frame; Dual-variable-isomorphic function; Isomorphic mean; Elastic mean; Cauchy mean value; Stolarsky mean