Univalency of certain analytic functions
type: Item
instance of: scholarly article
title: Univalency of certain analytic functions
zbMATH Open document ID: 1032.30010
published in: Proceedings of the Japan Academy. Series A
publication date: 2003-09-30T00:00:00Z
review text: Let \(\mathcal A\) be the class of functions that are analytic in the unit disc \({\mathcal U}=\{z:|z|<1\}\) and normalized such that \(f(0)=f'(0)-1=0.\) In this paper the authors introduce a subclass of \(\mathcal A,\) denoted by \({\mathcal T}(\lambda,\mu,g),\) and defined by: if \(g(z)\in {\mathcal A},\) with \(\frac{g(z)}{z}\neq 0,\) \(z\in{\mathcal U},\) \(\text{ Re} (\lambda) \geq 0\) and \(\mu>0\) then \(f(z)\in {\mathcal T}(\lambda,\mu,g)\) if and only if for all \(z\in {\mathcal U}\) \[ \frac{f(z)}{z}\neq 0 \] and \[ \left|z^2\left(\frac{f'(z)}{f^2(z)}-\frac{g'(z)}{g^2(z)}\right)-\lambda z^2\left(\frac{z}{f(z)}-\frac{z}{g(z)}\right)\right|<\mu. \] For this class the authors give a radius of univalence and necessary conditions for univalence and for that purpose they use some results from the theory of differential subordinations.
reviewed by: Nikola Tuneski
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1902577
zbMATH Keywords: analytic functions
zbMATH Keywords: univalent functions
zbMATH Keywords: univalence criteria
zbMATH Keywords: subordination
author: Dinggong Yang
author: Shigeyoshi Owa
MaRDI profile type: Publication
full work available at URL: pjaa.78.148
OpenAlex ID: W1996969531
cites work: Q3660033
cites work: Differential subordinations and univalent functions
cites work: One Criterion for Univalency
cites work: The Schwarzian Derivative and Univalent Functions
cites work: Some criteria for multivalently starlikeness
cites work: On a class of univalent functions
DOI: 10.3792/PJAA.78.148
description: scientific article; zbMATH DE number 1902577