Iterative roots of some functions

Authors : Sukrawan MAVECHA, Vichian LAOHAKOSOL, Boonrod YUTTANAN

Pages : 819-840

View : 8 | Download : 9

Publication Date : 0000-00-00

Article Type : Research Paper

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