Bulletin of the
Korean Mathematical Society BKMS

\noindent In this paper, we investigate uniqueness problemsof certain types of $q$-difference polynomials, which improve some results in \cite{zhang}. However, our proof is different from that in \cite{zhang}. Moreover, we obtain a uniqueness result in the case where $q$-differences of two entire functions share values as well. This research also shows that there exist two sets, such that for a zero-order non-constant meromorphic function $f$ and a non-zero complex constant $q$, $E(S_j, f)=E(S_j, \Delta_qf)$ for $j=1, 2$ imply $f (z)=t\Delta_qf$, where $t^n=1$. This gives a partial answer to a question of Gross concerning a zero order meromorphic function $f(z)$ and $\Delta_qf$.

Keywords: meromorphic functions, $Q$-difference, sharing value

MSC numbers: 30D35, 39A05