The polynomial-like iterative equation for PM functions

被引：0

作者：

LIU Liu ^{[1
]}

GONG XiaoBing ^{[2
]}

机构：

[1] Department of Mathematics, Southwest Jiaotong University

[2] Department of Mathematics, Neijiang Normal University

来源：

ScienceChina(Mathematics) | 2017年 / 60卷 / 08期

基金：

中国国家自然科学基金;

关键词：

functional equation; iteration; non-monotonicity; continuous solution; leading coefficient problem;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

The polynomial-like iterative equation is an important form of functional equations, in which iterates of the unknown function are linked in a linear combination. Most of known results were given for the given function to be monotone. We discuss this equation for continuous solutions in the case that the given function is a PM(piecewise monotone) function, a special class of non-monotonic functions. Using extension method, we give a general construction of solutions for the polynomial-like iterative equation.

引用

页码：1503 / 1514

页数：12

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