| 加权AM-GM-HM不等式链的加细 |
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| 引用本文： | 宋介珠,刘证. 加权AM-GM-HM不等式链的加细[J]. 纯粹数学与应用数学, 1999, 15(3): 59-62,72 |
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| 作者姓名： | 宋介珠 刘证 |
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| 作者单位： | 鞍山钢铁学院数理系,鞍山,114002 |
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| 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，还给出一个连接并且分离加权算术平均和加权调和平均的单调连续函数
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| 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 |
| 文章编号： | 1008-5513(1999)03-0059-62 |
| 修稿时间： | 1999-03-09 |
Refinement of weighted chain of AM-GM-HM inequalities |
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| SONG Jie zhu,LIU Zheng. Refinement of weighted chain of AM-GM-HM inequalities[J]. Pure and Applied Mathematics, 1999, 15(3): 59-62,72 |
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| Authors: | SONG Jie zhu LIU Zheng |
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| Abstract: | 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. |
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| Keywords: | arithmetic mean geometric mean harmonic mean weighted mean Ky Fan inequality Wang Wang inequality |
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