A class of univalent functions
type: Item
instance of: scholarly article
title: A class of univalent functions
zbMATH Open document ID: 0908.30009
published in: Hokkaido Mathematical Journal
publication date: 1999-03-18T00:00:00Z
review text: Let \(A\) denote the class of normalized analytic functions in the open unit disc \(U\) of the complex plane. Let \(S^*(\beta)\) denote functions in \(A\) which are starlike of order \(\beta\) and \(S^*= S^*(0)\). In this paper, the author investigates conditions on \(f\in A\) so that \(f\in S^*(\beta)\). For example if \(f\in A\) satisfies \[ \Biggl| f'(z)\Biggl({z\over f(z)}\Biggr)^{1+ \mu}- 1\Biggr|< \lambda \] with \(0< \mu< 1\) and \(0< \lambda\leq(1- \mu)/\sqrt{(1- \mu)^2+ \mu^2}\) then it is shown that \(f\in S^*\). The author also investigates conditions on \(f\) which ensures a certain integral operator acting on \(f\) belongs to \(S^*(\beta)\). The results are too complicated to be reproduced here.
reviewed by: V. Karunakaran
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1202947
zbMATH Keywords: starlike
author: M. Obradović
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1351001289
OpenAlex ID: W2011842897
DOI: 10.14492/HOKMJ/1351001289
description: scientific article; zbMATH DE number 1202947