连续单调不减函数迭代产生的数列的收敛性  

Convergence of the number sequence generated by iterations of the continuous and monotone-non-decreasing function

作　　者：成凯歌[1] CHENG Kaige(Department of Basis Course,Tourism College of Zhejiang,Hangzhou 311231,China)

机构地区：[1]浙江旅游职业学院基础部,浙江杭州311231

出　　处：《高师理科学刊》2022年第2期1-6,共6页Journal of Science of Teachers＇College and University

基　　金：浙江旅游职业学院优质课程资助项目(2017ZLY012)。

摘　　要：函数迭代是函数运算的重要内容,也是反映重复运动的重要数学模型,函数迭代产生的结果和函数本身的性质密切相关,越是复杂的函数迭代后往往会产生越复杂的结果,所以,函数迭代研究通常从简单函数开始.单调连续函数作为一类较简单的函数,它的迭代一直是迭代研究的重点内容之一,对定义在有限闭区间和无限区间上连续单调不减函数的迭代产生的数列进行讨论,证明了定义在有限闭区间上连续单调不减函数在定义域中任意一点的迭代产生的数列都收敛,给出了定义在无限区间上连续单调不减函数迭代产生的数列的收敛条件.The functional iteration is the important contents of function operation and an important mathematical model reflecting the repeated movement.The results of functional iteration are closely related to the nature of the function itself,the more complex results of iteration are produced by the more complex functions,thus,the researches of the functional iteration are usually began from the simple functions.The monotonic and continuous functions are considered as a simpler class of functions,its iterations are thought as one of the important issues of iterative research.By discussing the number sequence generated by iterations of the continuous and monotone-non-decreasing function defined on the finite closed interval or the infinite interval,it was obtained that the number sequence generated by iterations of the continuous and monotone-non-decreasing function defined on the finite closed interval is convergence at any point in domain,and the conditions of the convergence of the number sequence generated by iterations of the continuous and monotone-non-decreasing function defined on the infinite interval was given.

关 键 词：连续单调不减函数 迭代 数列 不动点 收敛 

分 类 号：O192[理学—数学]