Unicity of Entire Functions Concerning their $q-$ Derivatives-Difference-Polynomials

Abstract

In this paper, we study the unicity of entire functions concerning their $q-$shifts and $k-$th derivatives and prove: Let $f(z)$ be a transcendental entire function of zero-order, and $g(z)$ define as in (1.1). Let $a(z), b(z)$ be two distinct small functions of $f(z)$. If $f(z)$ and $g(z)$ share $a(z), b(z)$ IM, then $f(z)\equiv g(z)$.