| 几何算术平均不等式的初等证明与应用 |
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| 引用本文： | 邢家省,张愿章,陶鹏飞.几何算术平均不等式的初等证明与应用[J].河南科学,2007,25(3):353-357. |
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| 作者姓名： | 邢家省 张愿章 陶鹏飞 |
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| 作者单位： | 北京航空航天大学,数学系,数学、信息与行为教育部重点实验室,北京,100083;华北水利水电学院,郑州,450011;河南省泌阳县第一高级中学,河南,泌阳,463700 |
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| 基金项目： | 国家自然科学基金
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河南省软科学基金 |
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| 摘 要： | 几何平均算术平均不等式是非常重要的不等式.给出几何平均算术平均不等式的初等证明,这样就可使此不等式的使用大为提前,通过一些实例体现此不等式的使用价值.
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| 关 键 词： | 几何平均算术平均不等式 初等证明 不等式的应用 |
| 文章编号： | 1004-3918(2007)03-0353-05 |
| 修稿时间： | 2007-03-14 |
The Elementary Proof of Geometry Average Arithmetic Average Inequality and Its Applications |
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| XING Jia-sheng,ZHANG Yuan-zhang,TAO Peng-fei.The Elementary Proof of Geometry Average Arithmetic Average Inequality and Its Applications[J].Henan Science,2007,25(3):353-357. |
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| Authors: | XING Jia-sheng ZHANG Yuan-zhang TAO Peng-fei |
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| Institution: | 1. Department of Mathematics, LIMB of the Ministry of Education, Beihang University, Beijing 100083, China; 2. North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450011, China; 3. The No.1 Senior Middle School of Biyang County, Biyang 463700, China |
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| Abstract: | The geometry average arithmetic average inequality is very important in mathematical analysis.This paper provides the elementary proof of geometry average arithmetic average inequality,which can advance the use of the inequality significantly and can express its value through some applications. |
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| Keywords: | geometry average arithmetic average inequality elementary proof the use of inequality |
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