AbstractIn this paper, by using a technique of the first-order differential subordination, we find several sufficient conditions for an analytic function p such that $p(0)=1$
p
(
0
)
=
1
to satisfy $\operatorname{Re}\{ {\mathrm{e}}^{{\mathrm{i}}\beta } p(z) \} > \gamma $
Re
{
e
i
β
p
(
z
)
}
>
γ
or $| \arg \{p(z)-\gamma \} |<\delta $
|
arg
{
p
(
z
)
−
γ
}
|
<
δ
for all $z\in \mathbb{D}$
z
∈
D
, where $\beta \in (-\pi /2,\pi /2)$
β
∈
(
−
π
/
2
,
π
/
2
)
, $\gamma \in [0,\cos \beta )$
γ
∈
[
0
,
cos
β
)
, $\delta \in (0,1]$
δ
∈
(
0
,
1
]
and $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1 \}$
D
:
=
{
z
∈
C
:
|
z
|
<
1
}
. The results obtained here will be applied to find some conditions for spirallike functions and strongly starlike functions in $\mathbb{D}$
D
.
On Differential Subordination and Superordination for Univalent Function Involving New Operator
