Order of starlikeness for multipliers of univalent functions
type: Item
instance of: scholarly article
title: Order of starlikeness for multipliers of univalent functions
zbMATH Open document ID: 0558.30010
DOI: 10.1016/0022-247X(84)90155-0
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: A function \(f(z)=z-\sum^{\infty}_{n=2}a_ nz^ n\), \(| z| <1\) and \(a_ n\geq 0\) is in \(F(\{b_ n\})\) if \(\sum^{\infty}_{n=2}b_ na_ n\leq 1\) for the sequence of positive numbers \(\{b_ n\}\). The author shows that \(F(\{b_ n\})\) is a convex family of univalent functions if and only if \(b_ n\geq n\) for each n and that \((z-z^ n/b^ n)\) and the identity are the extreme points of the class; distortion and other mapping properties of the class are given. He also defines and examines the classes corresponding to \(F(\{b_ n\})\) when the coefficients \(a_ n\) are arbitrary complex numbers.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 3889858
zbMATH Keywords: starlike functions
zbMATH Keywords: coefficient multipliers
zbMATH Keywords: convex family of univalent functions
zbMATH Keywords: extreme points
author: H. Silverman
reviewed by: R.J.Libera
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3889858