| 凸函数的算子凸性估计及其在算子平均中的应用(英文) |
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| 引用本文： | 左红亮,段光才. 凸函数的算子凸性估计及其在算子平均中的应用(英文)[J]. 数学杂志, 2014, 34(1): 65-71 |
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| 作者姓名： | 左红亮 段光才 |
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| 作者单位： | 河南师范大学数学与信息科学学院 |
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| 基金项目： | Partially Supported by NSFC(10471085);the Basic Science and Technological Frontier Project of Henan Province(132300410261) |
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| 摘 要： | 本文利用Mond-Peari方法对凸函数的n个算子凸性进行了比式估计.在此基础上,得到了n个代数平均的幂与n个算子的幂的代数平均的比较,n个算子的几何平均的幂与n个算子的幂的几何平均的比较.特别地,文中还给出了代数平均和混序几何平均.
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| 关 键 词： | 算子凸 代数平均 几何平均 混序几何平均 |
| 收稿时间： | 2013-02-08 |
| 修稿时间： | 2013-05-07 |
BOUNDEDNESS OF OPERATOR CONVEXITY FOR CONVEX FUNCTIONS AND APPLICATIONS FOR OPERATOR MEANS |
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| ZUO Hong-liang and DUAN Guang-cai. BOUNDEDNESS OF OPERATOR CONVEXITY FOR CONVEX FUNCTIONS AND APPLICATIONS FOR OPERATOR MEANS[J]. Journal of Mathematics, 2014, 34(1): 65-71 |
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| Authors: | ZUO Hong-liang and DUAN Guang-cai |
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| Affiliation: | ZUO Hong-liang;DUAN Guang-cai;College of Mathematics and Information Science,Henan Normal University; |
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| Abstract: | In this paper, we estimate boundedness of operator convexity for convex functions. As an application, we obtain some relations between the power of operator means (arithmetic mean, geometric mean, chaotically geometric mean) and those means of operator powers. In particular, we obtain the order relation between arithmetic mean and chaotically geometric mean. |
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| Keywords: | operator convex arithmetic mean geometric mean chaotically geometric mean |
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