Some results for strongly starlike functions
type: Item
instance of: scholarly article
title: Some results for strongly starlike functions
zbMATH Open document ID: 0880.30012
author: Mamoru Nunokawa
author: Hitoshi Saitoh
author: Akira Ikeda
author: Naoya Koike
author: Shigeyoshi Owa
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-01-19T00:00:00Z
review text: Let \(\alpha\), \(0\leq \alpha<1\), \(\beta,0 <\beta <1\) be given. A function \(f(z)= z+ \dots\), is said to belong to the class of functions strongly starlike of order \(\beta\) and type \(\alpha\) in the unit disk \(D\) provided \(|\arg({zf'(z) \over f(z)}- \alpha)|<{\pi \over 2} \beta\) holds in \(D\). In the case \(\alpha=0\) such functions have been studied by \textit{J. Stakiewicz} [Ann. Univ. Mariae Curie-Skłodowska, Sect. A. 20 (1966) 59-75 (1971; Zbl 0247.30007), 20, 59-75 (1996; Zbl 0247.30007)]. The present authors derive here some sufficient conditions for \(f\) to belong to the class. Arguments are fairly straightforward.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1053553
reviewed by: Eligiusz Złotkiewicz
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5468
OpenAlex ID: W2037907825
cites work: Q5749519
cites work: On properties of non-Carathéodory functions
cites work: On the order of strongly starlikeness of strongly convex functions
cites work: A Criterion for Starlikeness
cites work: Q4338920
DOI: 10.1006/JMAA.1997.5468
description: scientific article; zbMATH DE number 1053553