On criteria for starlikeness and convexity of analytic functions
type: Item
instance of: scholarly article
title: On criteria for starlikeness and convexity of analytic functions
zbMATH Open document ID: 1087.30016
DOI: 10.1016/S0252-9602(17)30242-4
author: Nikola Tuneski
author: Vikramaditya Singh
published in: Acta Mathematica Scientia. Series B. (English Edition)
publication date: 2006-01-24T00:00:00Z
review text: Let \({\mathcal A}\) be the class of functions \(f(z)=z+\sum_{k=2}^\infty a_kz^k\) that are analytic in the unit disc \({\mathcal U}=\{z:| z| <1\}.\) In this paper the authors give criteria that imply starlikeness and convexity of the class \[ G_{\lambda,\gamma}=\left\{f\in {\mathcal A}: \left| \frac{1-\gamma+zf''(z)/f'(z)}{zf'(z)/f(z)}-(1-\gamma)\right| <\lambda, z\in {\mathcal U}\right\}. \] They also give sharp upper bound of \(| a_2| \) and of the Fekete-Szegö functional \(| a_3-\mu a_2^2| \) over this class. Special choices of \(\gamma\) lead to some previously known results and comparison with them is made.
reviewed by: Nikola Tuneski
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C50
zbMATH DE Number: 5000923
zbMATH Keywords: starlike
zbMATH Keywords: convex
zbMATH Keywords: criteria
zbMATH Keywords: Fekete-Szegö
MaRDI profile type: Publication
full work available at URL: s0252-9602(17)30242-4
OpenAlex ID: W2783200706
description: scientific article; zbMATH DE number 5000923