TY - JOUR
ID - 635
TI - Some results on value distribution of the difference operator
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Liu, Y.
AU - Wang, J. P.
AU - Liu, F. H.
AD - Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing, Zhejiang 312000, China
AD - Department of Mathematics, Shandon university, Jinan, Shandong 250100, China
Y1 - 2015
PY - 2015
VL - 41
IS - 3
SP - 603
EP - 611
KW - Meromorphic
functions
KW - difference equations
KW - uniqueness
KW - finite order
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_635.html
L1 - http://bims.iranjournals.ir/article_635_eb443301fa68e35139a83770ef545aa8.pdf
ER -