| 对算术-几何不等式的两种推广与改进 |
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| 引用本文： | 时统业,王辉.对算术-几何不等式的两种推广与改进[J].数学学习,2014(1):62-66. |
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| 作者姓名： | 时统业 王辉 |
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| 作者单位： | 海军指挥学院浦口分院;西安邮电大学自动化学院 |
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| 摘 要： | 将关于一组正数的加权算术-几何不等式推广为关于两组正数的改进型加权算术-几何不等式,其思路可为部分已有结论提供新的证明方法.突破关于自然对数的加权算术-几何不等式对具体函数的依赖,给出并证明了关于对数凸函数的加权算术-几何不等式.
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| 关 键 词： | 加权算术-几何平均 不等式 对数凸函数 |
Two Improvements of Arithmetic-geometric Mean Inequality |
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| SHI Tongye;WANG Hui.Two Improvements of Arithmetic-geometric Mean Inequality[J].Studies In College Mathematics,2014(1):62-66. |
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| Authors: | SHI Tongye;WANG Hui |
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| Institution: | SHI Tongye;WANG Hui;Pukou Institute,PLA Naval Command College;School of Automation,Xi’an University of Posts and Telcommunications; |
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| Abstract: | The weighted arithmetic-geometric mean inequality for one group of positive numbers is generalized to suit for two groups of positive numbers,and our approach can be used to prove some correlate theorems.Another weighted arithmetic-geometric mean inequality about logarithmic convex functions is shown also. |
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| Keywords: | weighted arithmetic-geometric mean inequality logarithmic convex function |
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