| 类对称函数的Schur凸性和不等式 |
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| 引用本文： | 龙波涌,褚玉明.类对称函数的Schur凸性和不等式[J].数学物理学报(A辑),2012,32(1):80-89. |
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| 作者姓名： | 龙波涌 褚玉明 |
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| 作者单位： | 1.湖州师范学院 数学系 浙江湖州 313000;
2.$安徽大学数学科学学院 合肥 230039 |
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| 基金项目： | 国家自然科学基金(11071069)和浙江省高等学校创新团队基金(T200924)资助 |
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| 摘 要： | 对x = (x1, x2,···, xn) ∈ (0,1)n 和 r ∈ {1, 2,···, n} 定义对称函数
Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1∑j=1r(1+xi3/1- xi3)1/r,
其中i1, i2, ···, ir 是整数. 该文证明了Fn(x, r) 是(0,1)n 上的Schur凸、Schur乘性凸和Schur调和凸函数. 作为应用,利用控制理论建立了若干不等式.
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| 关 键 词： | Schur凸 Schur乘性凸 Schur调和凸 |
| 收稿时间： | 2009-05-14 |
| 修稿时间： | 2011-05-29 |
The Schur Convexity and Inequalities for a Class of Symmetric Functions |
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| LONG Bo-Yong,CHU Yu-Ming.The Schur Convexity and Inequalities for a Class of Symmetric Functions[J].Acta Mathematica Scientia,2012,32(1):80-89. |
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| Authors: | LONG Bo-Yong CHU Yu-Ming |
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| Institution: | 1.Department of Mathematics, Huzhou Teachers College, Zhejiang Huzhou 313000;
2.College of Mathematics Science, Anhui University, Hefei 230039 |
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| Abstract: | For x = (x1, x2,···, xn) ∈ (0,1) and r ∈ {1, 2,···, n}, the symmetric function Fn(x, r) is defined by
Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1<i2<···<ir≤n ∑ j=1r(1+xi3/1- xi3)1/r,
where i1, i2, ···, ir are integers. In this paper, it is proved that Fn(x,r) is Schur convex, Schur multiplicatively convex and Schur harmonic convex on (0,1)n. As applications, some inequalities are established by use of the theory of majorization. |
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| Keywords: | Schur convexzz Schur multiplicatively convexzz Schur harmonic convexzz |
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