强一致收敛下弱几乎周期点和周期序列跟踪性的研究  

On the Weakly Almost Periodic Point and the Periodic Sequence Shadowing Property Under Strongly Uniform Convergence

作　　者：冀占江 张更容 JI Zhanjiang;ZHANG Gengrong(School of Data Science and Software Engineering∥Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System∥Guangxi Colleges and Universities Key Laboratory of Professional Software Technology, Wuzhou University, Wuzhou 543002, China;School of Mathematics and Computational Science, Hunnan First Normal University, Changsha 410205, China)

机构地区：[1]梧州学院大数据与软件工程学院/广西高校图像处理与智能信息系统重点实验室/广西高校行业软件技术重点实验室,梧州543002 [2]湖南第一师范学院数学与计算科学学院,长沙410205

出　　处：《华南师范大学学报（自然科学版）》2021年第2期110-113,共4页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11461002);广西壮族自治区自然科学基金项目(2020JJA110021);湖南省自然科学基金项目(2018JJ2074);2020年度广西壮族自治区高校中青年教师基础能力提升项目(2020KY17007);梧州学院校级重点项目(2020B007)。

摘　　要：在强一致收敛下,研究了弱几乎周期点和周期序列跟踪性,得到弱几乎周期点和周期序列跟踪性的若干结论:(1)设序列映射{f_(n)}强一致收敛于等度连续映射f,且点列{xk}是每个映射f_(n)的弱几乎周期点.若limk→x_(k)=x,则x是f的弱几乎周期点.(2)若序列映射{f_(n)}强一致收敛于等度连续映射f,则lim sup W(f_(n))W(f).(3)若f_(n)具有fine周期序列跟踪性,则f具有周期序列跟踪性.The weakly almost periodic point and the periodic sequence shadowing property are studied under strongly uniform convergence.Some conclusions about them are obtained.First,let the sequence map{f_(n)}converge strongly uniformly to the equicontinuous map f and the sequence of points{xk}be the weakly almost periodic point of every map f_(n).If limk→x_(k)=x,then the point x is the weakly almost periodic point of the map f.Second,if the sequence map{f_(n)}converges strongly uniformly to the equicontinuous map f,then limsup W(f_(n))W(f).Third,iff_(n) has the fine periodic sequence shadowing property,then f has periodic sequence shadowing property.

关 键 词：弱几乎周期点 周期序列跟踪性 等度连续 强一致收敛 

分 类 号：O189.11[理学—数学]