| 由Jensen不等式导出某些重要不等式 |
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| 引用本文： | 刘鸿雁.由Jensen不等式导出某些重要不等式[J].成都大学学报(自然科学版),2003,22(4):32-35. |
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| 作者姓名： | 刘鸿雁 |
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| 作者单位： | 四川邮电职业技术学院,成都,610067 |
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| 摘 要： | 不等式是研究分析数学的重要工具,很多常见不等式又是与函数的凸性分不开的 本文根据Jensen不等式,运用简捷的初等方法和恒等变形的技巧,导出一些重要不等式,再由凹函数f(x)=xα-αx(x>0,0<α<1)直接导出Young不等式
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| 关 键 词： | 凸函数 不等式 |
| 文章编号： | 1004-5422(2003)04-0032-04 |
Some Important Inequalities Could Be Deduced from Jensen Inequality |
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| LIU Hongyang.Some Important Inequalities Could Be Deduced from Jensen Inequality[J].Journal of Chengdu University (Natural Science),2003,22(4):32-35. |
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| Authors: | LIU Hongyang |
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| Abstract: | Inequality is an important tool to research analytical mathematies, and a lot of common inequality can not be separated from the convex quality of function. Here, based on Jensen Inequality, with the basic method of elementary equality and the variation of identical equation, some important inequalites. Then from concave function f(x)=x~α-αx(x>0, 0<α<1), the Young Inequality was deduced directly |
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| Keywords: | Convex function Inequality |
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