On multivalent starlike functions and Ozaki condition

ABSTRACT

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 .

KEYWORDS:

• Analytic functions
• univalent functions
• Ozaki’s condition

AMS SUBJECT CLASSIFICATIONS:

• Primary: 30C45
• Secondary: 30C80

Acknowledgements

This work was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge, Faculty of Mathematics and Natural Sciences, University of Rzeszów.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge, Faculty of Mathematics and Natural Sciences, University of Rzeszow.