引用本文:冀占江.强一致收敛条件下拟弱几乎周期性和序列跟踪性的研究[J].西南师范大学学报(自然科学版),2019,44(12):40~44
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强一致收敛条件下拟弱几乎周期性和序列跟踪性的研究
冀占江
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 梧州 543002
摘要:
在强一致收敛条件下研究了序列映射与极限映射之间关于拟弱几乎周期性和序列跟踪性的动力学性质.利用强一致收敛和等度连续的性质,得到如下结果:(i)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的拟弱几乎周期点,若limk→∞ xk=x,则xf的拟弱几乎周期点;(ii)若序列映射{fn}强一致收敛于等度连续映射f,则limn→∞ sup QWfn)⊂QWf);(iii)设序列映射{fn}强一致收敛于f,若fn具有fine序列跟踪性,则f具有序列跟踪性.这些结果丰富了强一致收敛条件下拟弱几乎周期性和序列跟踪性的理论.
关键词:  拟弱几乎周期点  序列跟踪性  等度连续  强一致收敛
DOI:10.13718/j.cnki.xsxb.2019.12.008
分类号:O189.11
基金项目:广西自然科学基金项目(2018JJB170034);广西高校中青年教师科研基础能力提升项目(2019KY0681);梧州学院校级科研项目(2017C001).
The Research of Quasi-weak Almost Periodic Property and Sequence Shadowing Property Under Strongly Uniform Convergence
JI Zhan-jiang
School of Data Science and Software Engineering/Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System, Wuzhou University, Wuzhou Guangxi 543002, China
Abstract:
The dynamical property of the quasi-weak almost periodic property and sequence shadowing property between the sequence map and the limit map under strongly uniform convergence have been studied in this paper. With the properties of the strong uniform convergence and equicontinuity, we get the following results:(i) Let the sequence map {fn} converges strongly uniformly to the equicontinuous map f and the sequence of points {xk} be the quasi-weak almost periodic point of every map fn. If limk→∞ xk=x, then the point x is the quasi-weak almost periodic point of the map f; (ii) If the sequence map {fn} converges strongly uniformly to the equicontinuous map f, then limn→∞ sup QW(fn)⊂QW(f); (iii) Let the sequence map {fn} converges strongly uniformly to the map f. If fn has the fine sequence shadowing property, then f has sequence shadowing property. These results enrich the theory of the quasi-weak almost periodic property and sequence shadowing property under strong uniform convergence.
Key words:  quasi-weak almost periodic point  sequence shadowing property  equicontinuous  strongly uniform convergence
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