Spiral-like functions with respect to a boundary point
type: Item
instance of: scholarly article
title: Spiral-like functions with respect to a boundary point
zbMATH Open document ID: 1018.30005
DOI: 10.1016/S0022-247X(02)00615-7
author: Dov Aharonov
author: Mark Elin
author: David Shoikhet
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: Some years ago \textit{M. S. Robertson} [ibid. 81, 327-345 (1981; Zbl 0472.30015)] started studying properties of functions analytic and univalent on the unit disk \(\Delta\) that map \(\Delta\) onto domains starlike w.r.t. a boundary point. Results in this direction were obtained also by \textit{A. Lyzzaik} [Proc. Am. Math. Soc. 91, 108-110 (1984; Zbl 0509.30009)], \textit{H. Silverman} and \textit{E. M. Sylvia} [Houston J. Math. 16, No. 2, 289-300 (1990; Zbl 0718.30007)]. The present authors in their interesting paper consider a more general situation: domains spiral-shaped w.r.t. a boundary point and univalent functions mapping \(\Delta\) onto such domains. They give a characterization of such functions and draw several conclusions.
reviewed by: Eligiusz Złotkiewicz
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1915602
zbMATH Keywords: spiral-shaped domains
zbMATH Keywords: spiral-like functions with respect to a boundary point
zbMATH Keywords: geometric characterization
zbMATH Keywords: spiral angle meaasure
MaRDI profile type: Publication
cites work: Q4944139
cites work: Dynamics of inequalities in geometric function theory
cites work: Holomorphically accretive mappings and spiral-shaped functions of proper contractions
cites work: Q4220703
cites work: On the class of functions starlike with respect to a boundary point
cites work: On a Conjecture of M. S. Robertson
cites work: Q4052427
cites work: Univalent functions starlike with respect to a boundary point
cites work: A Subordination Theorem for Ф-Like Functions
cites work: Semigroups in geometrical function theory
cites work: Q5749516
Recommended article: \(\delta\)-spirallike functions with respect to a boundary point
Recommended article: Q5212193
Recommended article: On a closely related class involving spirallike functions with respect to a boundary point
Recommended article: On a class of spiral-like functions with respect to a boundary point related to subordination
Recommended article: Region of variability for spiral-like functions with respect to a boundary point
Recommended article: A NOTE ON SPIRALLIKE FUNCTIONS
Recommended article: Q4761475
Recommended article: Q3349130
Recommended article: Q4591016
description: scientific article; zbMATH DE number 1915602