| Hlder不等式的初等证明及其应用 |
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| 引用本文： | 邢家省,郭秀兰,朱建设.Hlder不等式的初等证明及其应用[J].河南科学,2009,27(12):1484-1488. |
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| 作者姓名： | 邢家省 郭秀兰 朱建设 |
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| 作者单位： | 1. 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
2. 河南工业大学,理学院,郑州,450052 |
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| 基金项目： | 国家自然科学基金资助项目(10871016):北京市教育委员会共建项目专项资助 |
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| 摘 要： | 首先利用贝努利不等式给出了几何平均算术平均不等式的证明，其次给出了Young不等式和Young逆不等式的初等证明方法，进而给出了Holder不等式的初等证明，沟通了这些重要的不等式之间在初等数学阶段的联系．
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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 Hlder不等式 Minkowski不等式 |
An Elementary Proof of H(o)lder Inequality and Its Applications |
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| Xing Jiasheng,Guo Xiulan,Zhu Jianshe.An Elementary Proof of H(o)lder Inequality and Its Applications[J].Henan Science,2009,27(12):1484-1488. |
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| Authors: | Xing Jiasheng Guo Xiulan Zhu Jianshe |
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| Institution: | Xing Jiasheng, Guo Xiulan, Zhu Jianshe(1. Department of Mathematics, LMIB of the Ministry of Education, Beihang University, Beijing 100191, China; 2. College of Science, Henan University of Technology, Zhengzhou 450052, China) |
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| Abstract: | This paper presents the proof of geometric mean and arithmetic mean inequality by bernoull inequality. Then it gives the proof of Young inequality and gets the elementary proof of Holder inequality. So the link between these important inequalities are communicated in the elementary mathematical. |
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| Keywords: | Bernoull＇s inequality ceometric mean and arithmetic mean inequality Young＇s inequality Holder inequality： Minkowski inequality |
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