Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41320150615Some results on value distribution of the difference operator603611635ENY.LiuDepartment of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, ChinaJ. P.WangDepartment of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, ChinaF. H.LiuDepartment of Mathematics, Shandon university, Jinan, Shandong 250100, ChinaJournal Article20131218In 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 $k\geq 3$, (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.http://bims.iranjournals.ir/article_635_eb443301fa68e35139a83770ef545aa8.pdf