Sufficient conditions for spiral-likeness
type: Item
instance of: scholarly article
title: Sufficient conditions for spiral-likeness
zbMATH Open document ID: 0688.30009
DOI: 10.1155/S0161171289000797
author: H. Silverman
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46434
review text: The author gives an extension of the fact that \(\sum^{\infty}_{n=2}n| a_ n| \leq 1\) implies that \(f(z)=z+\sum^{\infty}_{n=2}a_ nz^ n\) is a starlike univalent function of the unit disk \({\mathbb{D}}\), namely if \[ \sum^{\infty}_{n=2}\frac{(n-1)+\sqrt{(n-1)^ 2+4n \cos^ 2 \lambda}}{2 \cos \lambda}| a_ n| \leq 1, \] then f is spirallike of order \(\lambda\), i.e., \[ Re(e^{i\lambda}(zf'(z))/(f(z)))>0\quad (z\in {\mathbb{D}}). \]
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C55
zbMATH DE Number: 4127556
zbMATH Keywords: Hadamard convolution
zbMATH Keywords: order of starlikeness
reviewed by: W. Koepf
MaRDI profile type: Publication
OpenAlex ID: W1983608850
description: scientific article; zbMATH DE number 4127556