加权算术——几何平均值不等式的控制证明

Majorized Proof of Weighted Arithmetic-geometric Means Inequality

众所周知,算术——几何平均值不等式是最基本、最重要的不等式,寻求它的不同证法,一直是人们研究的热点,至今已有上百种不同的证明方法。本文利用控制不等式的方法,并结合分析技巧给出加权算术——几何平均值不等式的一个新的证明。

As we all know,arithmetic-geometric mean inequalities are the most basic and important inequalities.To seek different method to prove them has been one of the study focuses and they have been proven by more than a hundred ways.By using methods based on the theory of majorization and combined with the analysis techniques,the weighted arithmetic-geometric means inequality is proved in a new way.