| 关于平方凸函数的积分型Jensen不等式 |
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| 引用本文： | 陈少元,宋振云.关于平方凸函数的积分型Jensen不等式[J].首都师范大学学报(自然科学版),2012,33(6):1-4. |
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| 作者姓名： | 陈少元 宋振云 |
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| 作者单位： | 湖北职业技术学院,湖北孝感,432000 |
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| 基金项目： | 湖北省教育科学“十一五”规划项目(2010B296) |
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| 摘 要： | 基于平方凸函数的平方凸性,研究了离散形式的Jensen不等式,运用定积分的定义、Henie定理及复合函数极限运算,得到了平方凸函数的积分型Jensen不等式;利用平方凸函数的一个充要条件,建立了平方凸函数的积分型Jensen不等式的推广形式.
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| 关 键 词： | 平方凸函数，充要条件，离散型Jensen不等式，积分型Jensen不等式 |
On Integral Jensen Inequality of Squared Convex Functions |
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| Chen Shaoyuan
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Song Zhenyun.On Integral Jensen Inequality of Squared Convex Functions[J].Journal of Capital Normal University(Natural Science Edition),2012,33(6):1-4. |
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| Authors: | Chen Shaoyuan Song Zhenyun |
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| Institution: | Chen Shaoyuan Song Zhenyun(Hubei Polytechnic Institute Xiaogan,Hubei 432000) |
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| Abstract: | Based on the squared convexity of square convex functions,after studying the discrete Jensen inequality,the authors find the integral Jensen inequality of squared convex functions by using the definition of definite integral,Henie theorem and the limit calculation of composite functions;and construct a more widely used expression by using of a necessary & sufficient condition of squared convex functions. |
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| Keywords: | square convex function necessary & sufficient condition discrete Jensen inequality integral Jensen inequality |
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