用构造法证明几种平均数关系及推广

The Constructive Method Proof of the Relationship amongSeveral 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|)r1r的特例。

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