| 单参数平均、对数平均和指数平均之间的一个精确的双向不等式(英文) |
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| 引用本文： | 王子奎,候守伟,褚玉明.单参数平均、对数平均和指数平均之间的一个精确的双向不等式(英文)[J].湖州师范学院学报,2011,33(1):1-6. |
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| 作者姓名： | 王子奎 候守伟 褚玉明 |
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| 作者单位： | 1. 杭州师范大学,数学系,浙江,杭州,310012
2. 湖州师范学院,理学院,浙江,湖州,313000 |
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| 基金项目： | This researchis supported by the Natural Science Foundation of China(11071069);the Innovation Team Foundation of the Depart ment of Education of Zhejiang Porvince(T200924) |
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| 摘 要： | 利用初等微分学比较了单参数平均与对数和指数平均的几何组合,发现了使得双向不等式Jp（a,b）1/2-3)/2]和所有a,b>0且a≠b成立的p的最大值和q的最小值,其中Jp（a,b）,L（a,b）和I（a,b）分别表示a与b的p-次单参数平均、对数平均和指数平均.
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| 关 键 词： | 单参数平均 对数平均 指数平均 |
A Sharp Double Inequality Between the One-Parameter, Logarithmic and Identric Means |
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| WANG Zi-kui,HOU Shou-wei,CHU Yu-ming.A Sharp Double Inequality Between the One-Parameter, Logarithmic and Identric Means[J].Journal of Huzhou Teachers College,2011,33(1):1-6. |
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| Authors: | WANG Zi-kui HOU Shou-wei CHU Yu-ming |
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| Institution: | 1.Department of Mathematics,Hangzhou Normal University,Hangzhou 310012,China;2.Faculty of Science,Huzhou Teachers College,Huzhou 313000,China) |
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| Abstract: | We compare the one-parameter mean with the geometric combination of logarithmic and identric means by use of the elementary differential calculus,and find the greatest value p=p(a) and the smallest value q = q(a)such that the double inequality Jp(a,b)＜ P(a,b)L1-a(a,b)＜Jq(a,b) holds for a∈ (0,√17-3/2] and all a,b＞0 with a≠b＜ where J p(a,b) ,L(a,b) and I(a,b) denote the p-th one-parameter,logarithmic,and identric means of a and b,respectively. |
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| Keywords: | one-parameter mean logarithmic mean identric mean |
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