Lorentz-Finsler范数中的不等式

IF 0.9 4区数学 Q2 MATHEMATICS

Mathematical Inequalities & Applications Pub Date : 2020-06-18 DOI:10.7153/mia-2021-24-26

N. Minculete, C. Pfeifer, N. Voicu

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引用次数: 4

摘要

我们证明了洛伦兹-芬斯勒几何为求解不等式提供了一个强有力的工具。为此，我们首先指出了一系列著名的不等式，如(加权的)算术几何平均不等式，Acz\ el不等式，Popoviciu不等式和Bellman不等式，分别是洛伦兹-芬斯勒几何中成立的逆三角形不等式的逆Cauchy-Schwarz的特殊情况。然后，我们用同样的方法证明了一些全新的不等式，包括Acz\ el不等式的两个改进。

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Inequalities from Lorentz-Finsler norms

We show that Lorentz-Finsler geometry offers a powerful tool in obtaining inequalities. With this aim, we first point out that a series of famous inequalities such as: the (weighted) arithmetic-geometric mean inequality, Acz\'el's, Popoviciu's and Bellman's inequalities, are all particular cases of a reverse Cauchy-Schwarz, respectively, of a reverse triangle inequality holding in Lorentz-Finsler geometry. Then, we use the same method to prove some completely new inequalities, including two refinements of Acz\'el's inequality.

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来源期刊

Mathematical Inequalities & Applications 数学-数学

CiteScore

2.30

自引率

10.00%

发文量

审稿时长

6-12 weeks

期刊介绍： ''Mathematical Inequalities & Applications'' (''MIA'') brings together original research papers in all areas of mathematics, provided they are concerned with inequalities or their role. From time to time ''MIA'' will publish invited survey articles. Short notes with interesting results or open problems will also be accepted. ''MIA'' is published quarterly, in January, April, July, and October.