On arclength problem for analytic functions
Let A be the class of functions g ( z ) = z + ∑ n = 2 ∞ a n z n which are analytic in the unit disk D = { z : | z | < 1 } . We denote by C ( r , g ) the closed curve which is the image of | z | = r < 1 under the mapping w = g ( z ) , furthermore we denote by L ( r , g ) the length of C ( r ,...
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Veröffentlicht in: | Analysis and mathematical physics 2023-06, Vol.13 (3), Article 45 |
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Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
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Zusammenfassung: | Let
A
be the class of functions
g
(
z
)
=
z
+
∑
n
=
2
∞
a
n
z
n
which are analytic in the unit disk
D
=
{
z
:
|
z
|
<
1
}
. We denote by
C
(
r
,
g
) the closed curve which is the image of
|
z
|
=
r
<
1
under the mapping
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. |
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ISSN: | 1664-2368 1664-235X |
DOI: | 10.1007/s13324-023-00806-w |