耦合不动点的迭代相关方法及其证明  

Study on Iterative Methods for Coupled Fixed Point

作　　者：赵云[1] 韩鑫 ZHAO Yun;HAN Xin(College of Mathematics and Computer Science,Yichun University,Yichun 336000,China)

机构地区：[1]宜春学院数学与计算机科学学院,江西宜春336000

出　　处：《宜春学院学报》2021年第3期38-41,62,共5页Journal of Yichun University

基　　金：江西省教育厅科技项目(项目编号:151029)。

摘　　要：在对半序集的定义及一些性质了解的前提下,本文给出半序集上集值算子的几种混合单调性的定义,并给出了集值映射下混合单调迭代序列的证明。再由半序拓扑空间上的一些性质,在不假设任何连续性的条件下,给出了单值和集值混合单调超限迭代序列收敛于耦合不动点的几个充分条件。On the premise of understanding the definition and some properties of semi-ordered sets,this paper gives the proof of the correlation theorem of mixed monotone iterative sequences under set-valued mappings on the definition of several mixed monotone operators on semi-ordered sets.Then,on the premise of understanding,some definitions and properties of semi-ordered topological Spaces,some sufficient conditions for mono-valued and set-valued mixed monotone transfinite iterative sequences to converge to the fixed point of coupling are given without assuming any continuity conditions.

关 键 词：超限迭代序列 耦合不动点 半序集 半序拓扑空间 

分 类 号：O177.91[理学—数学]