Classes of analytic functions subordinate to convex functions and extreme points
type: Item
instance of: scholarly article
title: Classes of analytic functions subordinate to convex functions and extreme points
zbMATH Open document ID: 1025.30011
DOI: 10.1016/S0022-247X(03)00257-9
author: K. T. Hallenbeck
author: David J. Hallenbeck
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-07-30T00:00:00Z
review text: Suppose that \(\Delta\) is the unit disk, \(D\) is a convex domain, \(D\neq\mathbb{C}\), \(0\in D\), \(F\) is an analytic and univalent mapping of \(\Delta\) onto \(D\). Let \(s(F)\) denote the set of all analytic functions \(f\) subordinate to \(F\) on \(\Delta\) and let \(Es(F)\) be the set of extreme points. The set \(s(F)\) is known when \(D\) is an infinite wedge, a strip, a half plane or a domain with smooth boundary and piecewise positive curvature but a full description of \(Es(F)\) otherwise is an open problem. Considering the open question the authors of this paper established two new sufficient conditions for \(f\) to be an extreme point of \(s(F)\).
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1957249
zbMATH Keywords: subordination
zbMATH Keywords: extreme point
zbMATH Keywords: extreme points
reviewed by: Eligiusz Złotkiewicz
MaRDI profile type: Publication
cites work: Extreme points of families of analytic functions subordinate to convex mappings
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cites work: Q3704135
cites work: On the Extreme Points of Some Sets of Analytic Functions
cites work: On extreme points of subordination families with a convex majorant
cites work: Q4844857
description: scientific article; zbMATH DE number 1957249