A new Roper-Suffridge extension operator on a Reinhardt domain
type: Item
instance of: scholarly article
title: A new Roper-Suffridge extension operator on a Reinhardt domain
zbMATH Open document ID: 1231.32001
DOI: 10.1155/2011/865496
author: Cailing Gao
author: Jianfei Wang
published in: Abstract and Applied Analysis
publication date: 2012-01-16T00:00:00Z
review text: Summary: We introduce a new Roper-Suffridge extension operator on the following Reinhardt domain \[ \Omega_{n,p_2,\dots,p_n} = \bigg\{z \in \mathbb C^n : |z_1|^2 + \sum^n_{j=2} |z_j|^{p_j} < 1\bigg\} \] given by \[ F(z) = \bigg(f(z_1) + f'(z_1) \sum^n_{j=2} a_j z^{p_j}_j\;,\; (f'(z_1))^{1/p_2} z_2\;,\; \dots, (f'(z_1))^{1/p_n} z_n\bigg)', \] where \(f\) is a normalized locally biholomorphic function on the unit disc \(\mathbb D\), \(p_j\) are positive integers, \(a_j\) are complex constants, and \(j = 2, \dots, n\). Some conditions for \(a_j\) are found under which the operator preserves almost starlike mappings of order \(\alpha\) and starlike mappings of order \(\alpha\), respectively. In particular, our results reduce to many well-known results when all \(a_j = 0\).
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 5997832
zbMATH Keywords: Reinhardt domain
zbMATH Keywords: Roper-Suffridge extension operator
Wikidata QID: Q58654505
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/865496
OpenAlex ID: W2006396161
cites work: Convex mappings on the unit ball of \(\mathbb C^ n\)
cites work: Univalent mappings associated with the Roper-Suffridge extension operator
cites work: Loewner chains and the Roper-Suffridge extension operator
cites work: A modification of the Roper-Suffridge extension operator
cites work: A generalization of half-plane mappings to the ball in ℂⁿ
cites work: Extreme points for convex mappings of \(B_n \)
cites work: Q5308935
cites work: A class of Loewner chain preserving extension operators
cites work: Q3016889
cites work: Modified Roper-Suffridge operator for some holomorphic mappings
cites work: On the Roper-Suffridge extension operator.
cites work: Q4804634
cites work: The generalized Roper-Suffridge extension operator
cites work: Q3371946
cites work: Q3631659
cites work: The growth theorem for starlike mappings on bounded starlike circular domains
cites work: The growth theorem for almost starlike mappings of order \(\alpha\) on bounded starlike circular domains
cites work: On the Grunsky inequalities for univalent functions
cites work: On decomposition theorem of normalized biholomorphic convex mappings in Reinhardt domains
description: scientific article; zbMATH DE number 5997832