| 一般化凸空间上的一个连续选择定理(英文) |
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| 引用本文： | 肖刚.一般化凸空间上的一个连续选择定理(英文)[J].数学杂志,2012,32(2):249-252. |
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| 作者姓名： | 肖刚 |
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| 作者单位： | 韩山师范学院数学与信息技术系,广东潮州,521041 |
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| 基金项目： | Supported by National Natural Science Foundation of China(60574075) |
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| 摘 要： | 本文研究一般化凸空间上的连续选择定理.利用在D■X的条件下,一般化凸空间(X,D;Γ)上Γ-凸子集的概念,得到了两类一般化凸空间之间,以及φ映射和Γ-凸映射之间的关系,并且得到了一个连续选择定理.本文推广了一般化凸空间上凸子集的概念.
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| 关 键 词： | 一般化凸空间 Γ-凸子集 Φ映射 连续选择定理 |
A CONTINUOUS SELECTION THEOREM ON GENERALIZED CONVEX SPACE |
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| XIAO Gang.A CONTINUOUS SELECTION THEOREM ON GENERALIZED CONVEX SPACE[J].Journal of Mathematics,2012,32(2):249-252. |
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| Authors: | XIAO Gang |
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| Institution: | XIAO Gang(Department of Math.and Information Technology,Hanshan Normal University,Chaozhou 521041,China) |
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| Abstract: | In this artilce,we discuss a continuous selection theorem on generalized convex space.Using the definition of Γ-convex set in a generalized convex space(X,D;Γ),where D is not necessarily a subset of X,we get the relationship between generalized convex spaces with D■X and generalized convex spaces with D■X,as well as the relationship between Φ-map and a multimap with nonempty Γ-convex values.Moreover,we also get a continuous selection theorem.We extend the conception of Γ-convex set in the generalized convex space. |
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| Keywords: | generalized convex space (Γ)-convex subset φ map continuous selection theorem |
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