| 凸函数和凹函数的幂平均不等式 |
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| 引用本文： | 曹小琴. 凸函数和凹函数的幂平均不等式[J]. 数学的实践与认识, 2000, 30(3): 363-366 |
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| 作者姓名： | 曹小琴 |
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| 作者单位： | 浙江金华教育学院数学系．金华 321000 |
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| 摘 要： | 文 [1 ]获得了当 α≥ 1时的凸函数的幂平均不等式 (3)、(4 ) [1] .本文指出文 [1 ]中的一个错误 ,并且得到了 α≤ 1时的凹函数的幂平均不等式 .修正和充实了文 [1 ]的定理 .同时讨论了当 α取其它值时不等式的情况 .
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| 关 键 词： | 凸函数 凹函数 幂平均不等式 |
| 修稿时间： | 1999-07-15 |
The Mean Value Inequality of the Power about the Convex Function and Concave Function |
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| CAO Xiao-qin. The Mean Value Inequality of the Power about the Convex Function and Concave Function[J]. Mathematics in Practice and Theory, 2000, 30(3): 363-366 |
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| Authors: | CAO Xiao-qin |
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| Abstract: | The mean value inequality of the power about the convex function (3)、 (4)[1] has been obtained when α≥1 in paper [1]. This paper points out an error in paper [1], It is in this paper that the author obtains the mean value inequality of power about the concave function when α≤1, corrects and enriches the theorem in paper [1], and also discusses the mean value inequality of the power in other cases of α. |
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| Keywords: | convex function concave function mean value inequality of power |
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