The polynomial-like iterative equation for PM functions

• DOI: 10.1007/s11425-016-0319-x
• Publication Date: 2017-06-06T14:48:57Z
• Authors: Liu Liu; XiaoBing Gong
• Keywords: Iterated function; Functional equation

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.