| 强一致收敛下弱几乎周期点和周期序列跟踪性的研究 |
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| 引用本文： | 冀占江,张更容. 强一致收敛下弱几乎周期点和周期序列跟踪性的研究[J]. 华南师范大学学报(自然科学版), 2021, 53(2): 110-113. DOI: 10.6054/j.jscnun.2021033 |
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| 作者姓名： | 冀占江 张更容 |
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| 作者单位： | 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;湖南第一师范学院数学与计算科学学院,长沙410205 |
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| 基金项目： | 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2018JJ20742020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 |
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| 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{fn}强一致收敛于等度连续映射f,且点列{xk}是每个映射fn的弱几乎周期点.若limk→∞xk=x,则x是f的弱几乎周期点.(2)若序列映射{fn}强一致收敛于等度连续映射f,则lim sup W(fn)...
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| 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 |
| 收稿时间： | 2020-08-05 |
On the Weakly Almost Periodic Point and the Periodic Sequence Shadowing Property Under Strongly Uniform Convergence |
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| Affiliation: | 1.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, China2.School of Mathematics and Computational Science, Hunnan First Normal University, Changsha 410205, China |
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| Abstract: | 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 {fn} converge strongly uniformly to the equicontinuous map f and the sequence of points{xk}be the weakly almost periodic point of every map fn. If $mathop {lim }limits_{k to infty } {x_k} = x$, then the point x is the weakly almost periodic point of the map f. Second, if the sequence map{fn}converges strongly uniformly to the equicontinuous map f, then limsup W(fn)?W(f). Third, if fn has the fine periodic sequence shadowing property, then f has periodic sequence shadowing property. |
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