%0 Journal Article
%T Some results on value distribution of the difference operator
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Liu, Y.
%A Wang, J. P.
%A Liu, F. H.
%D 2015
%\ 06/15/2015
%V 41
%N 3
%P 603-611
%! Some results on value distribution of the difference operator
%K Meromorphic
functions
%K difference equations
%K uniqueness
%K finite order
%R
%X In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(z)g(z)=t_2,$
for some constants $t_1$ and $t_2$ that satisfy $t_1^{n+1}=1$
and $t_2^{n+1}=1$. We generalize some previous results of Qi et. al.
%U http://bims.iranjournals.ir/article_635_eb443301fa68e35139a83770ef545aa8.pdf