区间上M型折线函数的一般迭代性质研究  

A Study on General Iterative Properties of M-shaped Polyline Function on Interval

作　　者：张福祥 ZHANG Fu-xiang(College of Mathematical Science,Chongqing Normal University,Shapingba 401331,Chongqing)

机构地区：[1]重庆师范大学数学科学学院,重庆沙坪坝401331

出　　处：《商洛学院学报》2025年第2期39-43,共5页Journal of Shangluo University

基　　金：重庆市教委科研项目(CXQT21014)。

摘　　要：通过研究折线函数的子区间,利用折线函数在子区间上的性质,同时结合线性函数的迭代公式,给出了折线函数在每一个子区间上经过迭代之后的一般表达式。利用折线函数迭代之后的表达式来判断折点的个数,证明了M型折线函数在迭代过程中折点个数保持不变和折点个数增加的定理,还给出了折线函数在满足某些条件下,折线函数经过迭代之后折点的坐标表达式和相关的不动点,进一步丰富了折线函数进行迭代的相关理论,能够更加简单判断M型折线函数迭代之后的折点个数情况和折点的坐标表达式。By studying the subintervals of polyline function and utilizing their properties within these intervals,combined with the iterative formulas of linear functions,a general expression for the polyline function after iteration in each subinterval is derived.This expression is then used to determine the number of break points,proving the theorem that for M-shaped polyline function,the number of break points remains constant or increases during iteration.Additionally,an expression for the coordinates of break points after iteration,under certain conditions,is provided,along with relevant fixed points.This enriches the theory of iterating polyline function,allowing for simpler assessments of the number of break points and their coordinates after iterations of M-shaped polyline function.

关 键 词：折线函数 折点 迭代 M型函数 

分 类 号：O193[理学—数学]