Iteration and Iterative Roots of Fractional Polynomial Function

Iteration is involved in the fields of dynamical systems and numerical computation and so forth. The computation of iteration is difficult for general functions (even for some simple functions such as linear fractional functions). In this paper, we discuss fractional polynomial function and use the method of conjugate similitude to obtain its expression of general iterate of order n under two different conditions. Furthermore, we also give iterative roots of order n for the function under two different conditions.