Values sharing results on q-difference and derivative of meromorphic functions

Abstract

In this paper, we mainly deal with the problem that f(qz) and $f'(z)$ share common values. One of the purpose is to explore whether the classical uniqueness results remain valid or not by considering some uniqueness theorems on f(qz) and $f'(z)$ sharing common values. Some examples and remarks are given to show that our results are sharp in certain senses. We also consider the entire solutions of the equation $f'(z)$ = f(qz), which is important for the uniqueness results.