偏序集上的数字不动点定理及其在单纯复形上的应用  

Digital Versions of Fixed Point Theorem in Partially Ordered Sets and Application to Simplicial Complex

作　　者：张丛磊[1,3] 张志国 ZHANG Cong-lei;ZHANG Zhi-guo(College of Arts and Sciences,Shanci Agricultural University,Jinzhong 030801,Shanxi,China;College of Mathematics and Computer Science,Shanxi Normal University,Linfen 041000,Shanxi,China;School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,Hebei,China)

机构地区：[1]山西农业大学文理学院,山西晋中030801 [2]山西师范大学数学与计算机科学学院,山西临汾041000 [3]河北师范大学数学科学学院,河北石家庄050024

出　　处：《山西师范大学学报（自然科学版）》2021年第3期30-34,共5页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：河北省高端人才引进项目.

摘　　要：本文给出了偏序集上的要求较弱收缩条件的Banach不动点定理并予以证明,该结论优化和改进了偏序集上的不动点定理和数字形式的不动点定理.本文接着研究了该结论在单纯复形模型上的应用.The present paper states and proves analogues of Banachs fixed point theorem in partially orderedsets which weaken the requirements on the contraction conditions.Fixed point theorem in partially ordered setsand digital versions of fixed point theorem are refined and improved.Then,an application to simplicial complexmodel is discussed.

关 键 词：数字度量空间 偏序集 不动点定理 单纯复形 

分 类 号：Q189.2[生物学—神经生物学]