| 凸函数与不等式 |
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| 引用本文： | 夏红卫. 凸函数与不等式[J]. 常州工学院学报, 2005, 18(1): 4-6 |
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| 作者姓名： | 夏红卫 |
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| 作者单位： | 常州工学院理学院,江苏,常州,213002 |
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| 摘 要： | 数学分析和研究中,许多最普通的不等式都起源于凸函数。本篇文章从凸函数的定义出发,得到函数的连续性,推导出Jensen不等式,并由此得到n个正数的算术平均与几何平均之间的不等式关系。
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| 关 键 词： | 凸函数 连续性 Jensen不等式 |
| 文章编号： | 1671-0436(2005)01-0004-03 |
| 修稿时间： | 2004-09-20 |
Convex Functions and Inequalities |
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| XIA Hong-wei. Convex Functions and Inequalities[J]. Journal of Changzhou Institute of Technology, 2005, 18(1): 4-6 |
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| Authors: | XIA Hong-wei |
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| Abstract: | Many of the most common inequalities in analysis have their origin in the notion of convexity. From the definition of the convex function, we obtain the function's continuation, induce Jensen's inequality, and obtain the familiar inequality between the arithmetic and geometric means of n positive numbers. |
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| Keywords: | convex function continuation Jensen's inequality |
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