涉及单位和的正数倒数之和与积的不等式的最佳常数

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-03-01 DOI:10.1186/s13660-024-03107-3

Yagub N. Aliyev

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引用次数: 0

摘要

本文研究了一个特殊的代数不等式，该不等式包含一个参数、倒数之和以及和为 1 的正实数的乘积，并利用新的优化论证确定了参数的最佳值。在三个数的情况下，这个代数不等式有一些有趣的几何应用，涉及欧拉不等式关于三角形外接圆和内接圆半径之比的推广。

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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The best constant for inequality involving the sum of the reciprocals and product of positive numbers with unit sum

In this paper, we study a special algebraic inequality containing a parameter, the sum of reciprocals and the product of positive real numbers whose sum is 1. Using a new optimization argument the best values of the parameter are determined. In the case of three numbers the algebraic inequality has some interesting geometric applications involving a generalization of Euler’s inequality about the ratio of radii of circumscribed and inscribed circles of a triangle.

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.