通过凸性和应用的均值之间的尖锐不等式

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-09-04 DOI:10.1016/j.bulsci.2025.103723

Duong Quoc Huy

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引用次数: 0

摘要

本文的目的是提供一种全新的方法，使我们能够推导出平均量之间不等式的一项细化和反转的最佳可能边界。这些结果涵盖并完善了文献中几乎所有的不平等。本文还讨论了矩阵均值不等式、矩阵的迹和行列式不等式以及酉不变范数和数值半径范数不等式的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Sharp inequalities between mean quantities via convexity and applications

The aim of the present paper is to provide a completely new method that allows us to derive the best possible bounds for one-term refinements and reverses of inequalities between mean quantities. These results cover and refine almost all inequalities in the literature. Applications to inequalities for matrix means, the traces and determinants of matrices, as well as inequalities for unitarily invariant norms and numerical radius norms, are also discussed.

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