类W-KKM (X,Y,Z), 几乎不动点定理和不动点定理

朴勇杰

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (5) : 665-671.

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PDF(333 KB)
系统科学与数学 ›› 2010, Vol. 30 ›› Issue (5) : 665-671. DOI: 10.12341/jssms08982
论文

类W-KKM (X,Y,Z), 几乎不动点定理和不动点定理

    朴勇杰
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Class W-KKM (X,Y,Z), Almost Fixed Point Theorems and Fixed Point Theorems

    PIAO Yongjie
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摘要

引进了相对弱R-子集和类(W-)KKM(X,Y,Z)的概念,给出了相对KKM映射与相对弱R-子集之间的等价关系以及W-KKM(X,Y,Z)的一个性质,然后给出了两个连续选择定理并得到不动点定理和重合点定理, 最后,在一致拓扑空间上得到具有弱-KKM性质的映射的几乎不动点,不动点和重合点的存在定理.

Abstract

The concepts of relatively weak R-subset and class (W-)KKM(X,Y,Z) were introduced, an equivalent relation of relative KKM map and relatively weak R-subset and a property of W-KKM(X,Y,Z) were given; and then two continuous selection theorem were given and from which, fixed point theorems and coincidence theorem were obtained; finally, existence theorems of
almost fixed point, fixed point theorem and coincidence point theorem for a map with weak-KKM property were obtained on uniform topological spaces.

关键词

相对弱R-子集 / 类(W-)KKM$(X / Y / Z)$ / Φ-映射 / 几乎不动点 / 重合点.

Key words

Relatively weak R-subset / class (W-)KKM$(X / Y / Z)$ / Φ-map / almost fixed point / coincidence point.

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朴勇杰. 类W-KKM (X,Y,Z), 几乎不动点定理和不动点定理. 系统科学与数学, 2010, 30(5): 665-671. https://doi.org/10.12341/jssms08982
PIAO Yongjie. Class W-KKM (X,Y,Z), Almost Fixed Point Theorems and Fixed Point Theorems. Journal of Systems Science and Mathematical Sciences, 2010, 30(5): 665-671 https://doi.org/10.12341/jssms08982
中图分类号: 47H05    47H10   
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