| 集值映射不动点的连续本质连通区 |
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| 引用本文： | 孙蕾,范晓冬.集值映射不动点的连续本质连通区[J].纺织高校基础科学学报,2007,20(1):17-19. |
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| 作者姓名： | 孙蕾 范晓冬 |
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| 作者单位： | 1. 渤海大学,信息科学与工程学院,辽宁,锦州,121013
2. 渤海大学,信息科学与工程学院,辽宁,锦州,121013;贵州大学,数学系,贵州,贵阳,550025 |
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| 摘 要： | 本质解的方法被广泛应用于各种问题解的稳定性研究,其在研究Nash平衡、不动点的稳定性中起着重要的应用.探讨了集值映射不动点的稳定性.引入了上半连续非空紧凸值集值映射不动点集的连续本质集的概念,并证明了其存在性.即证明了每一上半连续非空紧凸值集值映射至少存在一个该映射不动点集的极小连续本质集,以及该极小连续本质集是连通的.
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| 关 键 词： | 集值映射 不动点 本质连通区 |
| 文章编号： | 1006-8341（2007）01-0017-03 |
| 收稿时间： | 2006-12-16 |
| 修稿时间： | 2006年12月16 |
On the continuously essential components of fixed points for the set-valued mapping |
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| SUN Lei,FAN Xiao-dong.On the continuously essential components of fixed points for the set-valued mapping[J].Basic Sciences Journal of Textile Universities,2007,20(1):17-19. |
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| Authors: | SUN Lei FAN Xiao-dong |
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| Affiliation: | 1. College of Information Science and Engineering, Bohai University, Jinzhou, Liaoning 121013, China; 2. Department of Mathematics, Guizhou University, Guiyang 550025, China |
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| Abstract: | The method of essential solution has been widely used in various fields recently.It plays a crucial role in the study of stability of Nash equilibria,fixed point,etc.A further study on the stability is given.A concept of continuously essential sets of fixed points for upper semicontinuous mappings with nonempty,convex and compact values is introduced,and the existence of the continuously essential component is established.It is proved that there exist at least one minimal continuously essential set of fixed points,and the minimal continuously essential set is connected. |
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| Keywords: | set-valued mapping fixed point essential component |
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