Iterative roots of some functions

Authors : Sukrawan Mavecha, Vichian Laohakosol, Boonrod Yuttanan

Pages : 819-840

View : 9 | Download : 7

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :The iterative equation $f^{q}(x)=g(x)$, $x\in X$ for a given function $g$ and a positive integer $q$ is solved in the following two main cases: (i) $X=\mathbb{Z}$, $g(x)=ax+b$, ($a,b\in\mathbb{Z}$; $a\neq0,1$); (ii) $X=\mathbb{N}\cup\left\{ 0\right\} $, $g$ is increasing with no fixed point.
Keywords : Iterative functional equations, monotone functions, cycles