对标量和算子的对数和同等均值不等式的改进

J. Appl. Math. Pub Date : 2023-01-19 DOI:10.1155/2023/5195233

Aliaa Burqan, Abeer Abu-Snainah, Rania Saadeh

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引用次数: 1

摘要

在本文中，我们利用经典Hermite-Hadamard不等式的改进，给出了凸黎曼可积函数的改进不等式。将所得结果应用于特殊函数，建立了加权对数均值和加权等均值不等式的新改进。此外，根据标量不等式和算子的单调性，引入了相应的算子不等式。

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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Improvements of Logarithmic and Identric Mean Inequalities for Scalars and Operators

In this article, we provide refined inequalities for a convex Riemann’s integrable function using refinements of the classical Hermite-Hadamard inequality. The obtained results are applied on special functions to establish new improvements of inequalities on the weighted logarithmic mean and weighted identric mean. Moreover, corresponding operator inequalities are introduced based on the scalar inequalities and the monotonicity property for operators.

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J. Appl. Math.

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