Sets and value sharing of $q$-differences of meromorphic functions
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 731-745
https://doi.org/10.4134/BKMS.2013.50.3.731
Printed May 1, 2013
Xiao-Guang Qi and Lian-Zhong Yang
School of Mathematics, Shandong University
Abstract : \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
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