Certain Results for the Class of Carathéodory Functions
We present some sufficient conditions for an analytic function p in | z | < 1 in the complex plane to be in the class of Carathéodory functions, i.e. for Re { p ( z ) } > 0 in | z | < 1 . Several classes of functions may be described in terms of the class of Carathéodory functions. Therefor...
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| Veröffentlicht in: | Mediterranean journal of mathematics 2020-02, Vol.17 (1), Article 11 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We present some sufficient conditions for an analytic function
p
in
|
z
|
<
1
in the complex plane to be in the class of Carathéodory functions, i.e. for
Re
{
p
(
z
)
}
>
0
in
|
z
|
<
1
. Several classes of functions may be described in terms of the class of Carathéodory functions. Therefore, these conditions may be reformulated to various sufficient conditions for starlikeness, convexity, etc. |
|---|---|
| ISSN: | 1660-5446 1660-5454 |
| DOI: | 10.1007/s00009-019-1451-6 |