| 根平方平均的最优凸组合不等式 |
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| 引用本文： | 王勇.根平方平均的最优凸组合不等式[J].科技通报,2012,28(3):9-11. |
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| 作者姓名： | 王勇 |
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| 作者单位： | 河北民族师范学院数学与计算机系,河北承德,067000 |
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| 摘 要： | 本文得到最大值α和最小值β,使得对所有的a,b>0,a≠b双向不等式αC(a,b)+(1-α)A(a,b)
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| 关 键 词： | 算术平均 反调和平均 根平方平均 最优凸组合不等式 |
The Optimal Convex Combination Inequality for Root-square Mean |
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| WANG Yong.The Optimal Convex Combination Inequality for Root-square Mean[J].Bulletin of Science and Technology,2012,28(3):9-11. |
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| Authors: | WANG Yong |
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| Institution: | WANG Yong(Department of Mathematics and Computer,Hebei Teachers College for Nationalities,Chengde 067000,China) |
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| Abstract: | We find the greatest value α and the least value β such that the double inequality αC(a,b)+(1-α)A(a,b)0 with a≠b.Here A(a,b),B(a,b) and C(a,b) denote the arithmetic,contraharmonic and root-square means of two positive numbers a and b,respectively. |
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| Keywords: | arithmetic mean contraharmonic mean root-square mean optimal convex combination inequality |
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