加权AM-GM-HM不等式链的加细  

Refinement of weighted chain of AM GM HM inequalities

作　　者：宋介珠[1] 刘证[1] 

机构地区：[1]鞍山钢铁学院数理系,鞍山114002

出　　处：《纯粹数学与应用数学》1999年第3期59-62,72,共5页Pure and Applied Mathematics

摘　　要：在一定条件下得到加权的算术平均、几何平均和调和平均不等式链的一种加细形式，并由此推出加权的 ｋｙ Ｆａｎ 不等式和王王不等式．此外。A refinement of weighted chain of inequalities including the arithmetic, geometric and harmonic means is obtained under certain condition. As a consequence it implies the weighted inequalities of Ky Fan and Wang Wang. Furthermore, a monotonic continuous function joint and separate the weighted arithmetic mean and harmonic mean is given.

关 键 词：算术平均 几何平均 调和平均 加权平均 KYFAN不等式 王-王不等式 

分 类 号：O1[理学—数学] O29[理学—基础数学]