度量G-空间中的若干G-跟踪性  

Several G-Shadowing Properties in Metric G-spaces

作　　者：冀占江 陈占和[3] 刘海林 JI Zhanjiang;CHEN Zhanhe;LIU Hailin(School of Data Science and Sofiware Engineering,Wuzhou University,Wuzhou 543002,China;Guangxi Key Laboratory of Machine Vision and Intelligent Control,Wuzhou University,Wuzhou 543002,China;School of Mathematics and Information Science,Guangxi University,Nanning 543004,China;School of Science,Jiangxi University of Science and Technology,Ganzhou 341000,China)

机构地区：[1]梧州学院大数据与软件工程学院,广西梧州543002 [2]梧州学院广西机器视觉与智能控制重点实验室,广西梧州543002 [3]广西大学数学与信息科学学院,广西南宁5430004 [4]江西理工大学理学院,江西赣州341000

出　　处：《山西大学学报（自然科学版）》2024年第6期1127-1135,共9页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(12126415);广西自然科学基金(2020JJA110021);梧州学院校级重点项目(2020B007)。

摘　　要：在度量G-空间中研究了自映射f和迭代映射f^(k)在G-跟踪性、G-极限踪性和G-序列跟踪性上的关系,得到以下结果:(1)f具有G-跟踪性与f^(k)具有G-跟踪性是等价的;(2)f具有G-极限跟踪性与f^(k)具有G-极限跟踪性是等价的;(3)f具有G-序列跟踪性与f^(k)具有G-序列跟踪性是等价的。这些结果推广了度量空间中自映射f和迭代映射f^(k)关于跟踪性、极限踪性和序列跟踪性的结论。We studied the relations of G-shadowing property,G-limit shadowing property and G-sequence shadowing property between self-map f and iterative map f^(k)in metric G-spaces.Then,we drew the following conclusions:(1)it is an equivalent condition that f has the G-shadowing property and f^(k)has the G-shadowing property;(2)it is an equivalent condition that f has the G-limit shadowing property and f^(k)has the G-limit shadowing property;(3)it is an equivalent condition that f has the G-sequence shadowing property and f^(k)has the G-sequence shadowing property.The results improved the conclusions of shadowing property,limit shadowing property and sequence shadowing property between self-map f and iterative map f^(k)in metric space.

关 键 词：G-极限踪性 G-序列跟踪性 等价条件 可交换群 

分 类 号：O189.11[理学—数学]