平均值不等式再讨论

A new discussion on inequality of arithmetic and geometric means

将传统平均值不等式的求和项个数拓展到可变个,重新讨论了平均值不等式.通过定义体积函数,给出了体积函数的两个等价函数表示,来验证它的基本分析性质.

In the traditional inequality of arithmetic and geometric means,the number of items in the summation is fixed.The inequality is often used to solve extreme value problems.In this article,the number of summation terms is extended to be varying.In this situation,this inequality is revisited.Firstly,a volume function is defined.Next,two equivalent functions are given to verify the basic theoretical properties.