拓扑空间上的KKM定理,不动点定理,广义变分不等式

朴勇杰

系统科学与数学 ›› 2009, Vol. 29 ›› Issue (7) : 914-924.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2009, Vol. 29 ›› Issue (7) : 914-924. DOI: 10.12341/jssms08431
论文

拓扑空间上的KKM定理,不动点定理,广义变分不等式

    朴勇杰
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KKM Theorems, Fixed Point Theorems, Generalized Variational Inequalities on Topological Spaces

    PIAO Yongjie
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摘要

引进没有任何凸结构的拓扑空间上的广义R-KKM映射的定义并利用古典的KKM原理得到一般拓扑空间上的KKM型定理以及若干个变形结果,然后作为应用给出了非紧的拓扑空间上不动点定理和广义变分不等式解的存在性定理.

Abstract

The aim in this paper is to introduce the generalized R-KKM mapping in topological space without any convexity structure, and to use classical KKM principle to obtain KKM type theorems and their variant forms in general topological spaces. Then some fixed point theorems and existence theorem of solution for generalized variational inequality on non-compact general topological spaces as applications are given.

关键词

R-KKM映射 / R-子集 / 转移开[闭]映射 / 上半连续 / 广义变分不等式.

Key words

R-KKM map / R-subset / transfer open [closed] map / upper semicontinuous / generalized variational inequality.

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朴勇杰. 拓扑空间上的KKM定理,不动点定理,广义变分不等式. 系统科学与数学, 2009, 29(7): 914-924. https://doi.org/10.12341/jssms08431
PIAO Yongjie. KKM Theorems, Fixed Point Theorems, Generalized Variational Inequalities on Topological Spaces. Journal of Systems Science and Mathematical Sciences, 2009, 29(7): 914-924 https://doi.org/10.12341/jssms08431
中图分类号： 47H05    47H10   
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