The polynomial-like iterative equation for PM functions

发布时间：2018-02-24 12:13

  本文关键词： functional equation iteration non-monotonicity continuous solution leading coefficient problem　出处：《Science China(Mathematics)》2017年08期 　论文类型：期刊论文

【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.
[Abstract]: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.
【作者单位】： Department
【基金】：supported by National Natural Science Foundation of China (Grant No. 11501471) Fundamental Research Funds for the Central Universities (Grant No. 2682015BR017)
【分类号】：O175

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