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On the Isomorphic Means and Comparison Inequalities. (arXiv:2308.06500v1 [math.HO] CROSS LISTED)

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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.

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