Liu, Y., Wang, J., Liu, F. (2015). Some results on value distribution of the difference operator. Bulletin of the Iranian Mathematical Society, 41(3), 603-611.

Y. Liu; J. P. Wang; F. H. Liu. "Some results on value distribution of the difference operator". Bulletin of the Iranian Mathematical Society, 41, 3, 2015, 603-611.

Liu, Y., Wang, J., Liu, F. (2015). 'Some results on value distribution of the difference operator', Bulletin of the Iranian Mathematical Society, 41(3), pp. 603-611.

Liu, Y., Wang, J., Liu, F. Some results on value distribution of the difference operator. Bulletin of the Iranian Mathematical Society, 2015; 41(3): 603-611.

Some results on value distribution of the difference operator

^{1}Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, China

^{2}Department of Mathematics, Shandon university, Jinan, Shandong 250100, China

Abstract

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 $k\geq 3$, (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.