| 一个蕴含了诸多著名不等式的凸函数命题 |
| |
| 引用本文： | 王思聪.一个蕴含了诸多著名不等式的凸函数命题[J].贵州教育学院学报,2008,19(3):8-10. |
| |
| 作者姓名： | 王思聪 |
| |
| 作者单位： | 遵义师范学院数学系 贵州遵义563002 |
| |
| 摘 要： | 利用泰勒公式法证明一个凸函数命题，由该命题的结论可简单地导出几个熟知的重要不等式，如詹生（Jensen）不等式、算术-几何-调和平均不等式、杨氏（Young）不等式、霍尔德（Holder）不等式、柯西-希瓦兹（Cauchy—Schwartz）不等式等。
|
| 关 键 词： | 凸函数命题 泰勒公式法 不等式 |
| 文章编号： | 1002-6983(2008)03-0008-03 |
| 修稿时间： | 2007年8月27日 |
A convex function proposition containing some famous inequalities |
| |
| WANG Si-cong.A convex function proposition containing some famous inequalities[J].Journal of Guizhou Educational College(Social Science Edition),2008,19(3):8-10. |
| |
| Authors: | WANG Si-cong |
| |
| Institution: | WANG Si-cong (Department of Mathematics, Zunyi Normal College, Zunyi, Guizhou,563002 China) |
| |
| Abstract: | A convex function proposition is proved through using Taylor equation method.And from the conclusion of the proposition,some important inequalities can be derived simply;such as Jensen inequality,arithmetic-geometric-harmonic mean inequality,Young inequality,Holder inequality,the Cauchy-Schwartz inequality and so on. |
| |
| Keywords: | convex function Taylor equation inequality |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
