The polynomial-like iterative equation for PM functions

作者：Liu, Liu; Gong, XiaoBing^*

来源：Science China Mathematics, 2017, 60(8): 1503-1514.

DOI：10.1007/s11425-016-0319-x

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

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.

• 出版日期2017-8
• 单位内江师范学院; 西南交通大学