A note on Ozaki's condition

In this paper we consider another proof of the Ozaki's condition for multivalent functions that if f(z) is analytic in a convex domain D and for some real value α we have Re{eiαf(p)(z)}>0 in D, then f(z) is at most p-valent in D. Ozaki's condition is a generalization of the well-known N...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-06, Vol.534 (2), p.127860, Article 127860
Main Authors: Nunokawa, Mamoru, Sokół, Janusz
Format: Article
Language:English
Subjects:
Analytic functions
Multivalent
Univalent
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper we consider another proof of the Ozaki's condition for multivalent functions that if f(z) is analytic in a convex domain D and for some real value α we have Re{eiαf(p)(z)}>0 in D, then f(z) is at most p-valent in D. Ozaki's condition is a generalization of the well-known Noshiro-Warschawski univalence condition.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127860