迭代修复含有限个同类型间断函数的连续性

刘晓华, 罗世超

数学学报 ›› 2022, Vol. 65 ›› Issue (1) : 123-146.

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数学学报 ›› 2022, Vol. 65 ›› Issue (1) : 123-146. DOI: 10.12386/A2022sxxb0010
论文

迭代修复含有限个同类型间断函数的连续性

    刘晓华, 罗世超
作者信息 +

Continuity of Functions with Finitely Many Discontinuities of the Same Type Repaired by Iteration

    Xiao Hua LIU, Shi Chao LUO
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文章历史 +

摘要

我们已证明具有一个间断点的函数有连续的二次迭代.它实际上表明在迭代之下它的间断点能被自己函数对修复为连续点.如果一个函数含至少两个间断点,那么,在迭代之下,它的间断点或者被它自己函数对修复为连续点或者被其它间断点的函数对修复为连续点.本文研究具有多于一个但是只含有限个同类型间断点的不连续函数,给出了这些函数二次迭代连续的充分必要条件.

Abstract

It was proved that a function with exact one discontinuity may have a continuous iterate of second order. It actually shows that its discontinuity may be repaired to be a continuous one by its own pair of functions under iteration. If a function has at least two discontinuities, then each of its discontinuities may be repaired to be a continuous one by either its own pair of functions or the other's pair of functions under iteration. In this paper we investigate those functions having more than one but finitely many discontinuities of the same type and give necessary and sufficient conditions for those functions whose second order iterates are continuous.

关键词

迭代 / 连续性 / 同类型间断点

Key words

iteration / continuity / discontinuities of the same type

引用本文

导出引用
刘晓华, 罗世超. 迭代修复含有限个同类型间断函数的连续性. 数学学报, 2022, 65(1): 123-146 https://doi.org/10.12386/A2022sxxb0010
Xiao Hua LIU, Shi Chao LUO. Continuity of Functions with Finitely Many Discontinuities of the Same Type Repaired by Iteration. Acta Mathematica Sinica, Chinese Series, 2022, 65(1): 123-146 https://doi.org/10.12386/A2022sxxb0010

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基金

四川省教育厅重点科研基金项目(18ZA0242);乐山师范学院重点项目(LZD014)

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