| 几何凸函数的几何平均型Hadamard不等式 |
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| 引用本文： | 宋振云,涂琼霞.几何凸函数的几何平均型Hadamard不等式[J].首都师范大学学报(自然科学版),2011,32(4):14-17. |
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| 作者姓名： | 宋振云 涂琼霞 |
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| 作者单位： | 1. 湖北职业技术学院信息技术学院,湖北孝感,432000
2. 湖北职业技术学院财经学院,湖北孝感,432000 |
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| 基金项目： | 湖北省高等学校教学研究项目(20060422) |
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| 摘 要： | 考虑几何凸函数的几何凸性,针对几何凸函数的几何平均,利用几何凸函数的Jensen型不等式,应用定积分的定义及分部积分法,得到了几何凸函数的几何平均型Hadamard不等式,并给出了简单应用.
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| 关 键 词： | 几何凸函数 Jensen不等式 Hadamard不等式 α次幂积分平均 几何平均 |
Geometric Mean-type Hadamard Inequality of Geometric Convex Function |
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| Song Zhenyun,Tu Qiongxia.Geometric Mean-type Hadamard Inequality of Geometric Convex Function[J].Journal of Capital Normal University(Natural Science Edition),2011,32(4):14-17. |
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| Authors: | Song Zhenyun Tu Qiongxia |
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| Institution: | Song Zhenyun1 Tu Qiongxia2(1.School of Information and Technology,Hubei Polytechnic Institute Xiaogan,Hubei 432000,2.School of Finance and Economy,Hubei 432000) |
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| Abstract: | According to the geometric mean of geometric convex function,the geometric mean-type Hadamard inequality of geometric convex function is derived and the simple application is also elicited by considering the geometric convexity of geometric convex function and applying the Jensen-type inequality of geometric convex function as well as the definition of definite integral and integration by parts. |
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| Keywords: | geometric convex function Jensen-type inequality Hadamard-type inequality α th power integral mean geometric mean |
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