Sharp bounds for the difference between the arithmetic and geometric means

被引:0
|
作者
J. M. Aldaz
机构
[1] Universidad Autónoma de Madrid,Departamento de Matemáticas
来源
Archiv der Mathematik | 2012年 / 99卷
关键词
26D15; Variance; Arithmetic-geometric inequality;
D O I
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学科分类号
摘要
We present sharp bounds for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sum_{i=1}^n \alpha_i x_i -\prod_{i=1}^n x_i^{\alpha_i} }$$\end{document} in terms of the variance of the vector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(x_1^{1/2},\dots,x_n^{1/2})}$$\end{document}.
引用
收藏
页码:393 / 399
页数:6
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