On the Isomorphic Means and Comparison Inequalities

08/12/2023

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by   Liu Yuan, et al.

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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.