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| 摘要: |
| 本文通过已有的公共不动点存在性定理, 利用Fort定理研究了Hausdorff拓扑向量空间紧凸集上的集值映射族公共不动点集的通有稳定性, 即证明了在Baire分类意义下, 存在一个稠密剩余子集使得公共不动点问题是本质的, 从而是稳定的. |
| 关键词: 公共不动点 广义等度KKM映射族 稠密剩余集 通有稳定性 |
| DOI： |
| 分类号:O177.91 |
| 基金项目:国家自然科学基金项目 (71961003); 贵州省科技厅联合基金项目 (黔科合 LH 字(2017)7223); 贵州大学博士基金 (贵大人基合字(2019) 49) |
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| THE GENERIC STABILITY OF COMMON FIXED POINTS SET |
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mo chunrong,yang yanlong
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| Abstract: |
| In this paper, we study the generic stability of common fixed points of set-valued mappings on compact and convex sets of Hausdorff topological vector spaces by using a known result. We prove that there exists a dense residual subset such that the mappings are essential and, hence, the common fixed points set is stable in the sense of Baire classification. |
| Key words: Commom fixed point generalized equi-KKM family of set-valued mappings dense residual set generic stability |
