Abstract
AbstractIn this paper we study some properties of functions f which are analytic and normalized (i.e. $$f(0)=0=f'(0)-1$$
f
(
0
)
=
0
=
f
′
(
0
)
-
1
) such that satisfy the following subordination relation $$\begin{aligned} \left( \frac{zf'(z)}{f(z)}-1\right) \prec \frac{z}{(1-pz)(1-qz)}, \end{aligned}$$
z
f
′
(
z
)
f
(
z
)
-
1
≺
z
(
1
-
p
z
)
(
1
-
q
z
)
,
where $$(p,q) \in [-1,1] \times [-1,1]$$
(
p
,
q
)
∈
[
-
1
,
1
]
×
[
-
1
,
1
]
. These types of functions are starlike related to the generalized Koebe function. Some of the features are: radius of starlikeness of order $$\gamma \in [0,1)$$
γ
∈
[
0
,
1
)
, image of $$f\left( \{z:|z|<r\}\right) $$
f
{
z
:
|
z
|
<
r
}
where $$r\in (0,1)$$
r
∈
(
0
,
1
)
, radius of convexity, estimation of initial and logarithmic coefficients, and Fekete–Szegö problem.
Funder
University of Turku (UTU) including Turku University Central Hospital
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Algebra and Number Theory,Analysis
Reference35 articles.
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