The Fixed Points of Solutions of Some q -Difference Equations

Abstract

The purpose of this paper is to investigate the fixed points of solutions $f(z)$ of some $q$-difference equations and obtain some results about the exponents of convergence of fixed points of $f(z)$ and $f(q^{j}z)(j\in {\mathbb{N}}_{+})$, $q$-differences ${\mathrm{\Delta }}_{q}f(z)=f(qz)-f(z)$, and $q$-divided differences ${\mathrm{\Delta }}_{q}f(z)/f(z)$.