Abstract
A multidimensional recurring mean inequality is shown. Furthermore, we prove some new inequalities, which can be considered to be the extensions of those established inequalities, including, for example, the Polya-Szego and Kantorovich inequalities.
Highlights
The theory of means and their inequalities is fundamental to many fields including mathematics, statistics, physics, and economics.This is certainly true in the area of probability and statistics
In 6, the author proves the mean inequality of two random variables
The purpose of the present paper is to establish a recurring mean inequality, which generalizes the mean inequality of two random variables to n random variables
Summary
A multidimensional recurring mean inequality is shown. We prove some new inequalities, which can be considered to be the extensions of those established inequalities, including, for example, the Polya-Szegoand Kantorovich inequalities.
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