| 度量凸函数的延拓 |
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| 引用本文： | 林国琛,张文.度量凸函数的延拓[J].数学研究,2010,43(2):162-166. |
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| 作者姓名： | 林国琛 张文 |
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| 作者单位： | 1. 厦门理工学院数理系,福建,厦门,361024
2. 厦门大学数学科学学院,福建,厦门,361005 |
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| 基金项目： | 厦门理工学院引进人才项目 |
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| 摘 要： | 每个度量空间都能等距嵌入到实Banach空间，所以度量凸函数可视为Banach空间子集上的函数．本文举出反例说明不是所有度量凸函数都能延拓为凸函数，并给出度量凸函数能延拓为凸函数的充分条件．
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| 关 键 词： | 度量凸度量空间 度量凸函数 凸函数 |
Extensions of Metrically Convex Functions |
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| Lin Guochen,Zhang Wen.Extensions of Metrically Convex Functions[J].Journal of Mathematical Study,2010,43(2):162-166. |
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| Authors: | Lin Guochen Zhang Wen |
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| Institution: | 1.Department of Mathematics and Physics; Xiamen University of Technology, Xiamen Fujian361024; 2.School of Mathematical Sciences,Xiamen University, Xiamen Fujian361005) |
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| Abstract: | Every metric space is isometric to a subset of a real Banach space, so metrically convex functions can be regarded as functions on subsets of real Banach spaces. In the paper, we give an antiexample to explain that not all metrically convex functions can be extended to convex functions, and give some sufficient conditions under which metrically convex functions can be extended to convex functions. |
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| Keywords: | metrically convex metric space metrically convex function convex function |
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