| 加权算术——几何平均值不等式的控制证明 |
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| 引用本文： | 张鉴,石焕南.加权算术——几何平均值不等式的控制证明[J].北京联合大学学报(自然科学版),2011,25(4):46-47. |
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| 作者姓名： | 张鉴 石焕南 |
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| 作者单位： | 北京联合大学师范学院电气信息系,北京,100011 |
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| 基金项目： | 2010年度北京市教育委员会科技计划面上项目 |
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| 摘 要： | 众所周知,算术——几何平均值不等式是最基本、最重要的不等式,寻求它的不同证法,一直是人们研究的热点,至今已有上百种不同的证明方法。本文利用控制不等式的方法,并结合分析技巧给出加权算术——几何平均值不等式的一个新的证明。
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| 关 键 词： | 加权算术——几何平均值不等式 控制 Schur-凹 初等对称函数 |
Majorized Proof of Weighted Arithmetic-geometric Means Inequality |
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| ZHANG Jian,SHI Huan-nan.Majorized Proof of Weighted Arithmetic-geometric Means Inequality[J].Journal of Beijing Union University,2011,25(4):46-47. |
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| Authors: | ZHANG Jian SHI Huan-nan |
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| Institution: | (Department of Electric information,Teachers’ College of Beijing Union University,Beijing 100011,China) |
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| Abstract: | As we all know,arithmetic-geometric mean inequalities are the most basic and important inequalities.To seek different method to prove them has been one of the study focuses and they have been proven by more than a hundred ways.By using methods based on the theory of majorization and combined with the analysis techniques,the weighted arithmetic-geometric means inequality is proved in a new way. |
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| Keywords: | Weighted arithmetic-geometric means inequality Majorization Schur-concave Elementary symmetric function |
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