算术和几何平均值之间的差异的界限及其在不等式中的应用,Symmetry

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算术和几何平均值之间的差异的界限及其在不等式中的应用
Symmetry ( IF 2.2 ) Pub Date : 2021-12-12 , DOI: 10.3390/sym13122398
Shigeru Furuichi , Nicuşor Minculete

许多论文都研究了对加权算术几何平均不等式的改进和反转。在本文中，我们使用已知的不等式为加权算术平均值和几何平均值之间的差异提供了一些界限。我们改进了 Furuichi-Ghaemi-Gharakhanlu 和 Sababheh-Choi 给出的结果。我们还给出了一些熵的界限，以不同的方法应用结果。在^{第 4 节中}，我们探讨了某些凸函数或凹函数，它们是轴上的对称函数

吨 = 1 / 2

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Bounds for the Differences between Arithmetic and Geometric Means and Their Applications to Inequalities

Refining and reversing weighted arithmetic-geometric mean inequalities have been studied in many papers. In this paper, we provide some bounds for the differences between the weighted arithmetic and geometric means , using known inequalities. We improve the results given by Furuichi-Ghaemi-Gharakhanlu and Sababheh-Choi. We also give some bounds on entropies, applying the results in a different approach. In ^{Section 4}, we explore certain convex or concave functions, which are symmetric functions on the axis

t = 1 / 2

更新日期：2021-12-13

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