一个平均不等式的反向及其类似

Reversion and Analogy of a Mean Inequality

在最近的几百年中,关于多个正数的算术平均和几何平均的差的估计,是平均不等式研究中的一个持续热点.本文利用最值压缩定理,给出了算术平均和几何平均的差的两个新的估计,部分地回答了J.M.Aldaz一个公开问题.

Ia mean inequalities research, the estimation involving the difference between arithmetic mean and geometric mean in variables is continuous for hundreds of years. By means of compressed independent variables theorem, this paper gives the new upper bound of the difference between arithmetic mean and geometric mean, and partly solves an open problem put forward by J. M. Aldaz.