In this paper we consider the iterative equation G（x, f（x）,..., f^n（x）） = F（x） on R, and give the existence of C^1 solutions near the fixed point of F, which generalize some results on the leading coefficient ...In this paper we consider the iterative equation G（x, f（x）,..., f^n（x）） = F（x） on R, and give the existence of C^1 solutions near the fixed point of F, which generalize some results on the leading coefficient problem from the form of the polynomial-like iterative equations to the general form.展开更多
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 functio...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.展开更多
基金Supported by the Youth Foundation of Sichuan University (Grant No. 2008123)
文摘In this paper we consider the iterative equation G（x, f（x）,..., f^n（x）） = F（x） on R, and give the existence of C^1 solutions near the fixed point of F, which generalize some results on the leading coefficient problem from the form of the polynomial-like iterative equations to the general form.
基金supported by National Natural Science Foundation of China (Grant No. 11501471)Fundamental Research Funds for the Central Universities (Grant No. 2682015BR017)
文摘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.
