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| 实解析函数在极值点附近的凹凸性 | |
| 引用本文： | 孙刘平,周展宏. 实解析函数在极值点附近的凹凸性[J]. 广东海洋大学学报, 2006, 26(3): 64-67 |
| 作者姓名： | 孙刘平 周展宏 |
| 作者单位： | 1. 常州纺织服装职业技术学院数学教研室,江苏,常州,213164 2. 广东海洋大学理学院,广东,湛江,524025 |
| 摘 要： | 讨论了一类实解析函数在极小(大)值点附近存在凸(凹)性区间的条件,得到了如下主要结果:若非常值函数y=f(x)在x0处取得极小(大)值,且在x0的某一邻域G内实解析的,则存在x0的一小邻域G*G,使得原函数在G*上为凸(凹)的。 |
| 关 键 词： | 极值点 凸函数 实解析 |
| 文章编号： | 1007-7995(2006)03-0064-04 |
| 修稿时间： | 2005-10-28 |
Concavity-Convexity of Functions near Extreme Points |
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| SUN Liu-ping,ZHOU Zhan-hong. Concavity-Convexity of Functions near Extreme Points[J]. Journal of Zhanjiang Ocean University, 2006, 26(3): 64-67 | |
| Authors: | SUN Liu-ping ZHOU Zhan-hong |
| Abstract: | In this paper,under what conditions there is a domain is discussed in which the given real analytic function near the minimum(maximum) point is convex(concave).A main result is gained as follows: if the non-constant function of one variable y=f(x) gets minimum(maximum) at point x_0,and is real analytic in some neighborhood G of x_0,then there exists a smaller neighborhood G~*G of x_0 such that the given function is convex(concave). |
| Keywords: | extreme point convex function real analysis |
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