Author:
Wang Xin-Li,Xu Hong-Yan,Zhan Tang-Sen
Abstract
Abstract
In this paper, we deal with the zeros of the q-shift difference-differential polynomials
[
P
(
f
)
∏
j
=
1
d
f
(
q
j
z
+
c
j
)
s
j
]
(
k
)
−
α
(
z
)
and
(
P
(
f
)
∏
j
=
1
d
[
f
(
q
j
z
+
c
j
)
−
f
(
z
)
]
s
j
)
(
k
)
−
α
(
z
)
, where
P
(
f
)
is a nonzero polynomial of degree n,
q
j
,
c
j
∈
C
∖
{
0
}
(
j
=
1
,
…
,
d
) are constants,
n
,
d
,
s
j
(
j
=
1
,
…
,
d
)
∈
N
+
and
α
(
z
)
is a small function of f. The results of this paper are an extension of the previous theorems given by Chen and Chen and Qi. We also investigate the value sharing for q-shift difference polynomials of entire functions and obtain some results which extend the recent theorem given by Liu, Liu and Cao.
MSC:39A50, 30D35.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis