泛系关系族的泛对称与不动泛系定理
Pansymmetry and Fixed Pansystems Theorems of a Class of Pansystems Relations
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摘要: 本文在泛系方法论的框架下,将泛对称与不动泛系定理的一些结果推广到了二元关系族的情形.具体地讨论了对于有限论域上的一族二元关系何时存在公共的不动子集的问题,得到了几个确定二元关系族是否存在公共的不动子集的简括的判别定理.其结果推广了传统的不动点理论中有关映射族是否存在公共的不动点的主要判别定理——Markov-Kakutani定理.Abstract: In this paper, some results of pansymmetry and fixed pansy stems theorems are extended to the case of a class of binary relations under the framework of pansystems methodology. It is concretely discussed when a class of binary relations has a common fixedsubset on a finite universal set. Several simple but comprehensive decisive theorems are obtained which can be determined if a class of binary relations has a common fixed subset. As a result. the mum decisive theorem——Markov-Kakutani Theorem——is extended, which is in traditionally fixed point theory and can be determined if a class of mappings has a common fixed point.
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[1] Wu Xue-mou.Pansystems Methodology:concepts.theorems and applications(Ⅰ)-(Ⅵ).Science Exploration.1.2,4(1982),1,4(1983).1(1984) [2] Wu Xue-mou.Fixed pansystems theorems and pansystems catastrophe analysis of panweighted network,J.Math.Research and Exposition.1(1984). [3] 吴学谋,泛系方法论与泛系突变分析,《中国力学学会分岔、突变、稳定性学术会议论文汇编》(1983). [4] Smart.D.R.,Fixed Point Theorems.Cambridge University Press(1980). -
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