Iterative roots of some functions

Authors

SUKRAWAN MAVECHA
VICHIAN LAOHAKOSOL
BOONROD YUTTANAN

DOI

10.3906/mat-1612-67

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

First Page

819

Last Page

840

Recommended Citation

MAVECHA, SUKRAWAN; LAOHAKOSOL, VICHIAN; and YUTTANAN, BOONROD (2018) "Iterative roots of some functions," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 8. https://doi.org/10.3906/mat-1612-67
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/8