SETS AND VALUE SHARING OF q-DIFFERENCES OF MEROMORPHIC FUNCTIONS

Title & Authors
SETS AND VALUE SHARING OF q-DIFFERENCES OF MEROMORPHIC FUNCTIONS
Qi, Xiao-Guang; Yang, Lian-Zhong;

Abstract
In this paper, we investigate uniqueness problems of certain types of $\small{q}$-difference polynomials, which improve some results in [20]. However, our proof is different from that in [20]. Moreover, we obtain a uniqueness result in the case where $\small{q}$-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 $\small{f}$ and a non-zero complex constant $\small{q}$, $\small{E(S_j,f)=E(S_j,{\Delta}_qf)}$ for $\small{j=1,2}$ imply $\small{f(z)=t{\Delta}_qf}$, where $\small{t^n=1}$. This gives a partial answer to a question of Gross concerning a zero order meromorphic function $\small{f(z)}$ and $\small{t{\Delta}_qf}$.
Keywords
meromorphic functions;Q-difference;sharing value;
Language
English
Cited by
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