Growth and distortion results for a class of biholomorphic mapping and extremal problem with parametric representation in \(\mathbb{C}^n\)

DOI10.1007/s11785-018-00881-zzbMath1429.32008arXiv1910.09150OpenAlexW2907808040MaRDI QIDQ2007938

Zhen-Han Tu, Liangpeng Xiong

Publication date: 22 November 2019

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.09150

zbMATH Keywords

Roper-Suffridge extension operatorstar-like mappingsdistortion estimatesbiholomoprhic mappings on the unit ball

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Other generalizations of function theory of one complex variable (32A30)

Related Items (5)

Distortion results for a certain subclass of biholomorphic mappings in ℂⁿ ⋮ Unnamed Item ⋮ Distortion theorems for classes of \(g\)-parametric starlike mappings of real order in \(\mathbb{C}^n\) ⋮ Loewner chains applied to \(g\)-starlike mappings of complex order of complex Banach spaces ⋮ Bounds of all terms of homogeneous expansions for a subclass of \(g\)-parametric biholomorphic mappings in \(\mathbb{C}^n\)

Cites Work

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• Sharp distortion theorems for a subclass of biholomorphic mappings which have a parametric representation in several complex variables
• An extension operator associated with certain \(G\)-Loewner chains
• Schwarz lemma at the boundary of the unit ball in \(\mathbb C^n\) and its applications
• On the sharp distortion theorems for a subclass of starlike mappings in several complex variables
• Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation
• Extreme points, support points and \(g\)-Loewner chains associated with Roper-Suffridge and Pfaltzgraff-Suffridge extension operators
• Distortion theorems for convex mappings on homogeneous balls
• Support point functions and the Loewner variation
• Extension operators for locally univalent mappings
• The Schwarz lemma at the boundary of the symmetrized bidisc
• Convex mappings on the unit ball of \(\mathbb C^ n\)
• Extreme points, support points and the Loewner variation in several complex variables
• Extremal properties associated with univalent subordination chains in \(\mathbb C^n\)
• Subordination chains and univalence of holomorphic mappings in C\(^n\)
• Shearing process and an example of a bounded support function in \(S^0(\mathbb B^2)\)
• Bounded support points for mappings with \(g\)-parametric representation in \(\mathbb{C}^2\)
• Starlike and convex mappings in several complex variables
• The Schwarz lemma at the boundary
• Growth and Distortion Results for Convex Mappings in Infinite Dimensional Spaces
• On support points of the class $S^0(B^n)$
• Φ-Like Holomorphic Functions In C n and Banach Spaces
• A Distortion Theorem for Biholomorphic Mappings in ℂ 2
• Parametric Representation of Univalent Mappings in Several Complex Variables
• The growth theorems for subclasses of biholomorphic mappings in several complex variables

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