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.

DOI

10.3906/mat-1612-67

Keywords

Iterative functional equations, monotone functions, cycles

First Page

819

Last Page

840

Recommended Citation

MAVECHA, S, LAOHAKOSOL, V, & YUTTANAN, B (2018). Iterative roots of some functions. Turkish Journal of Mathematics 42 (3): 819-840. https://doi.org/10.3906/mat-1612-67

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