The polynomial-like iterative equation for PM functions

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2017,（8）
• 页码范围: 1503-1514
• 页数: 12页
• 语种: 英文
• DOI: 10.1007/s11425-016-0319-x

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.