| 从贝努利不等式到Hlder不等式的演变过程及应用 |
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| 引用本文： | 邢家省,王洪志.从贝努利不等式到Hlder不等式的演变过程及应用[J].吉首大学学报(自然科学版),2010,31(2):10-14. |
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| 作者姓名： | 邢家省 王洪志 |
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| 作者单位： | （北京航空航天大学数学与系统科学学院,数学、信息与行为教育部重点实验室,北京100191) |
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| 基金项目： | 国家自然科学基金资助项目（10771011） |
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| 摘 要： | 首先利用贝努利不等式给出几何平均算术平均不等式的证明,然后给出Young不等式和Young逆不等式的初等证明方法,进而给出Holder不等式的初等证明,并将这些结果应用到一些重要不等式的证明.
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| 关 键 词： | 贝努利不等式 几何平均算术平均不等式 Young不等式 Holder不等式 Minkowski不等式 |
Development from Bernoulli Inequality to Hlder Inequality and Its Applications |
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| XING Jia-Sheng,WANG Hong-Zhi.Development from Bernoulli Inequality to Hlder Inequality and Its Applications[J].Journal of Jishou University(Natural Science Edition),2010,31(2):10-14. |
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| Authors: | XING Jia-Sheng WANG Hong-Zhi |
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| Institution: | (Department of Mathematics,LMIB of the Ministry of Education,Beihang University,Beijing 100191,China) |
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| Abstract: | This paper presents the proof of geometric mean and arithmetic mean inequality by Bernoulli inequality.Then it gives the proof of Young inequality and gets the elementary proof of Hlder inequality.And some important inequalities can be proved by those results. |
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| Keywords: | Bernoulli&rsquo s inequality geometric mean and arithmetic mean inequality Young&rsquo s inequality Hlder inequality Minkowski inequality |
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