Coefficient inequalities for a subclass of starlike functions
type: Item
instance of: scholarly article
title: Coefficient inequalities for a subclass of starlike functions
zbMATH Open document ID: 0584.30008
DOI: 10.1016/0022-247X(85)90364-6
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The authors investigate subclasses of the well known class S of univalent functions. \(T^*(a,b)\subset S\) is the subclass of functions \(f\in S\) satisfying for \(| z| <1:\) \[ | (zf'(z)/f(z))-a| \leq b,\quad a\quad real\quad and\quad b\geq 0 \] s.t. \(f(z)=z- \sum^{\infty}_{n=2}a_ nz^ n\), \(a_ n\geq 0\). The author finds various properties of these classes like coefficients' estimates, extreme points and connections with the class of \(\alpha\)-starlike functions. The class \(T^*_ 2(a,b)\subset T^*(a,b)\) is the class of functions in \(T^*(a,b)\) where \(a<1\) and \(a_{2k+1}=0\) for \(k\geq 1\). Further results are proved also for this class. Most of the results are sharp.
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C50
Mathematics Subject Classification ID: 30C70
zbMATH DE Number: 3935384
zbMATH Keywords: positive coefficients
zbMATH Keywords: class S
zbMATH Keywords: extreme points
zbMATH Keywords: \(\alpha \) -starlike functions
author: Robert D. Berman
author: H. Silverman
MaRDI profile type: Publication
cites work: Univalent Functions with Negative Coefficients
Recommended article: Coefficient Inequalities for certain Starlike and Convex functions
Recommended article: Coefficient bounds for certain subclasses of starlike functions
Recommended article: Coefficient inequality for a subclass of pre starlike functions
Recommended article: Q5433810
Recommended article: Coefficient inequalities for univalent starlike functions
Recommended article: Q3712544
Recommended article: Coefficient inequality for \(q\)-starlike functions
Recommended article: On coefficient estimates for a certain class of starlike functions
Recommended article: Some inequalities for starlike functions
Recommended article: Q6042976
description: scientific article; zbMATH DE number 3935384