Abstract
AbstractLet $${\mathcal {A}}$$
A
be the class of functions $$\begin{aligned} g(z)=z+\sum _{n=2}^{\infty }a_nz^n \end{aligned}$$
g
(
z
)
=
z
+
∑
n
=
2
∞
a
n
z
n
which are analytic in the unit disk $${\mathbb {D}}=\{z:|z|<1\}$$
D
=
{
z
:
|
z
|
<
1
}
. We denote by C(r, g) the closed curve which is the image of $$|z|=r<1$$
|
z
|
=
r
<
1
under the mapping $$w=g(z)$$
w
=
g
(
z
)
, furthermore we denote by L(r, g) the length of C(r, g). In this paper we are interested in finding the maximum of the length L(r, f) as f(z) runs through all members of a fixed class of functions.
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Algebra and Number Theory,Analysis