| 对数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. 对数凸函数的几何平均型Hadamard不等式[J]. 湖南理工学院学报：自然科学版, 2011, 0(1) |
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| 作者姓名： | 宋振云 涂琼霞 |
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| 作者单位： | 湖北职业技术学院信息技术学院;湖北职业技术学院财经学院; |
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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： | 考虑对数凸函数的对数凸性,针对对数凸函数的几何平均,利用对数凸函数的Jensen不等式,应用定积分的定义,通过定积分运算,得到了对数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： | 对数凸函数 Jensen型不等式 算术平均 几何平均 Hadamard不等式 |
Geometric Mean-type Hadamard Inequality of Logarithmic Convex Function |
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| SONG Zhen-yun,TU Qiong-xia. Geometric Mean-type Hadamard Inequality of Logarithmic Convex Function[J]. Journal of Hunan Institute of Science and Technology, 2011, 0(1) |
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| Authors: | SONG Zhen-yun TU Qiong-xia |
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| Affiliation: | SONG Zhen-yun1,TU Qiong-xia2(1.School of Information and Technology,Hubei Polytechnic Institute,Xiaogan 432000,China,2.School of Finance and Economy,China) |
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| Abstract: | According to the geometric mean of logarithmic convex function,the geometric mean-type Hadamard inequality of logarithmic convex function is derived and the simple application is also elicited by considering the logarithmic convexity of logarithmic convex function and applying the Jensen-type inequality of logarithmic convex function as well as the definition and operation of definite integral. |
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| Keywords: | logarithmic convex function jensen-type inequality arithmetic mean geometric mean Hadamard-type inequality |
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