A new criterion for starlike functions
type: Item
instance of: scholarly article
title: A new criterion for starlike functions
zbMATH Open document ID: 0849.30007
DOI: 10.1155/S0161171296000865
author: Ling Yi
author: Shusen Ding
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1996-06-30T00:00:00Z
full work available at URL: https://eudml.org/doc/47524
review text: Let \(A\) be the class of functions \(f\), which are holomorphic in the unit disc \(D= \{z: |z|< 1\}\), with \(f(0)= f'(0)- 1= 0\). Let \(S^*\) be the set of starlike functions: \[ S^*= \{f\in A, \text{Re}(zf'(z)/f(z))> 0, z\in D\}. \] \textit{R. Singh} and \textit{S. Singh} [Proc. Am. Math. Soc. 106, No. 1, 145-152 (1989; Zbl 0672.30007)] proved that if \(f\in A\) and \(\text{Re}(f'(z)+ zf''(z))> - 1/4\), \(z\in D\), then \(f\in S^*\). In the present paper, it is proved that if \(f\in A\) and \(\text{Re}(f'(z)+ zf''(z))> 1- 3/[4(1- \ln 2)^2+ 2]\approx - 0,263\), \(z\in D\), then \(f\in S^*\).
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C55
zbMATH DE Number: 894098
zbMATH Keywords: starlike functions
reviewed by: Zbigniew Jerzy Jakubowski
MaRDI profile type: Publication
OpenAlex ID: W1972682827
description: scientific article; zbMATH DE number 894098