| 弱向量变分不等式解集的连通性 |
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| 引用本文： | 黄龙光,刘三阳.弱向量变分不等式解集的连通性[J].数学学报,2005,48(2):339-342. |
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| 作者姓名： | 黄龙光 刘三阳 |
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| 作者单位： | [1]集美大学理学院,厦门361021／／西安电子科技大学应用数学系，西安710071 [2]西安电子科技大学应用数学系，西安710071,厦门361021／／西安电子科技大学应用数学系，西安710071 |
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| 基金项目： | 国家自然科学基金资助项目(69972036) |
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| 摘 要： | 研究拓扑向量空间到连续线性映射空间映射的弱向量变分不等式和与之相关 的纯量型变分不等式解集的关系, 引入弱和强一致连续概念,利用纯量型变分不等式 解集所表征的集值映射的特性给出弱向量变分不等式解集连通的一个充分条件。
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| 关 键 词： | 弱向量变分不等式 弱一致连续 强一致连续 |
The Connectedness of Solution Set for the Weak Vector Variational Inequality |
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| Long Guang HUANG School of Science,Jimei University,Xiamen ,P. R. China.The Connectedness of Solution Set for the Weak Vector Variational Inequality[J].Acta Mathematica Sinica,2005,48(2):339-342. |
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| Authors: | Long Guang HUANG School of Science Jimei University Xiamen P R China |
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| Institution: | Long Guang HUANG School of Science, Jimei University, Xiamen 361021, P. R. China Department of Applied Mathematics, Xidian University, Xi'an 710071, P. R. China San Yang LIU Department of Applied Mathematics, Xidian University, Xi'an 710071, P. R. China |
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| Abstract: | The relationship between weak vector variational inequality with a mapping from a topological vector space to continuous linear mapping space and its scalarization is discussed. A sufficient condition is presented on the connectedness of solution set for the weak vector variational inequality in a topological vector space. The conceptions of weakly and strongly uniformly continuous are introduced. The result on connectedness is derived by discussing the properties of set-valued mapping induced by solution set of a scalar variational inequality related to the weak vector variational inequality. |
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| Keywords: | Vector variational inequality Weakly uniformly continuous Strongly uniformly continuous |
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