关于A-G的几个新的上下界

On New Upper and Lower Bounds of A-G

对于给定区间上的n个正数,它们的算术平均A和几何平均G的差的估计,一直是不等式理论研究中最基础的一部分.最值压缩定理已成为研究多元不等式的一种常用方法,作为最值压缩定理应用之一,给出了A-G的四个新的上下界,其中的一些强于相应的已知结果.

For n variables in a given interval,we let difference of arithmetic mean and geometric mean be A-G and then the estimation of A-G has always been one most basic part in the theoretical study of inequality.Compressed independent variables theorem has become a common method to study inequality.This paper is an application of compressed independent variables theorem and here we give some new upper and lower bounds for A-G.Some results improve the known-inequalities respectively.