| 广义向量似变分不等式解集的通有稳定性及本质连通区的存在性 |
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| 引用本文： | 杨辉,俞建.广义向量似变分不等式解集的通有稳定性及本质连通区的存在性[J].系统科学与数学,2002,22(1):090-095. |
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| 作者姓名： | 杨辉 俞建 |
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| 作者单位： | 1. 浙江大学应用数学系,杭州,310027,贵州大学数学系,贵阳,550025
2. 贵州省科学技术厅,贵阳,550002 |
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| 基金项目： | 国家自然科学基金（10061002），贵州省自然科学基金，贵州大学科学基金资助课题． |
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| 摘 要： | 本文研究广义向量似变分不等式解集的稳定性．证明了在满足一定的连续性和凸 性条件的广义向量似变分不等式问题构成的空间Ｍ中，大多数（在Ｂａｉｒｅ分类意下）广 义向量似变分不等式问题的解集是稳定的，并证明了Ｍ中的每个广义向量似变分不等式 的解集至少存在一个本质连通区。
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| 关 键 词： | 广义向量似变分不等式(GVVLIP) usco映射 本质解 本质连通区 |
| 修稿时间： | 2000年9月4日 |
THE GENERIC STABILITY AND THE EXISTENCE OF ESSENTIAL COMPONENTS OF THE SOLUTION SETS FOR GENERALIZED VECTOR VARIATIONAL-LIKE INEQUALITIES |
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| Hui YANG,Jian YU.THE GENERIC STABILITY AND THE EXISTENCE OF ESSENTIAL COMPONENTS OF THE SOLUTION SETS FOR GENERALIZED VECTOR VARIATIONAL-LIKE INEQUALITIES[J].Journal of Systems Science and Mathematical Sciences,2002,22(1):090-095. |
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| Authors: | Hui YANG Jian YU |
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| Institution: | (1)Dept.of Applied Math.,Zhejiang Univ.,Hangzhou 310027,P.R.CHina,Department of Mathematics,Guizhou University, Guiyang 550025,P.R.China;(2)Science and Technology Department of Guizhou Province, Guiyang 550002,P.R.China |
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| Abstract: | In this paper, we study the stability of the solution sets for generalized vector variational-like inequality problems. We prove that, in the space M consisting of generalized vector variational-like inequality problems satisfying some convexity and continuity conditions, most generalized vector variational-like inequality problems (in the sense of Baire category) have stable solution sets, and that for each problem in M, its solution set possesses at least one essential component. |
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| Keywords: | Generalized vector variational-like inequality problem (GVVLIP) usco map-ping essential solution essential component |
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