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Properties of q-shift difference-differential polynomials of meromorphic functions
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Journal Article
Properties of q-shift difference-differential polynomials of meromorphic functions
2014
Overview
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 International Publishing,Springer Nature B.V
