关于几种平均数关系的构造法证明及推广

The Constructive Method Proof of the Relationship among Several Averages and Generalization

调和平均数、几何平均数和算术平均数之间存在单调非减关系 ,并且可将它们归结为幂平均数的一些特殊形式 利用构造法可给出这种关系的证明及推广 ,指出幂平均数是统计函数 [E(｜Z｜) r]1r

There is nondecreasing relationship among arithmetic average, geometrical average and harmonic average.The three averages can be given by power average. In this paper we find that power average is a special example of statistical function 1r by constructive method.