On multivalent starlike functions and Ozaki condition

We prove some new sufficient conditions for function to be p-valent, or p-valently starlike in the unit disc. We extend in some sense the Ozaki condition which says that if for some real , then is at most p-valent in a convex domain .

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Bibliographic Details
Published in:	Complex variables and elliptic equations Vol. 64; no. 1; pp. 78 - 92
Main Authors:	Nunokawa, Mamoru, Sokół, Janusz
Format:	Journal Article
Language:	English
Published:	Colchester Taylor & Francis 02.01.2019 Taylor & Francis Ltd
Subjects:	Analytic functions Ozaki's condition Primary: 30C45 Secondary: 30C80 univalent functions
ISSN:	1747-6933, 1747-6941
Online Access:	Get full text
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Description
Summary:	We prove some new sufficient conditions for function to be p-valent, or p-valently starlike in the unit disc. We extend in some sense the Ozaki condition which says that if for some real , then is at most p-valent in a convex domain .
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1747-6933 1747-6941
DOI:	10.1080/17476933.2017.1419209