Löwner chains and a subclass of biholomorphic mappings

DOI10.1016/j.jmaa.2006.10.036zbMath1126.30011OpenAlexW2045386689MaRDI QIDQ996893

Qing-Hua Xu, Tai Shun Liu

Publication date: 19 July 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.10.036

zbMATH Keywords

Roper-Suffridge extension operatorstarlike mappinglocally biholomorphic mappingalmost starlike mapping of order \(\alpha\)spirallike mapping of type \(\alpha\)

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45)

Related Items (15)

Support points for families of univalent mappings on bounded symmetric domains ⋮ Loewner chain associated with the modified Roper-Suffridge extension operator ⋮ Löwner chains and a subclass of bi-univalent functions ⋮ Extreme points, support points and \(g\)-Loewner chains associated with Roper-Suffridge and Pfaltzgraff-Suffridge extension operators ⋮ Some geometrical properties of free boundaries in the Hele-Shaw flows ⋮ Extremal Problems for Mappings with g-Parametric Representation on the Unit Polydisc in ℂ n ⋮ Distortion theorems for almost convex mappings of order \(\alpha\) in several complex variables ⋮ Almost spirallike mappings of type and complex order on the unit ball ⋮ Analytic and geometric properties associated with some extension operators ⋮ \(g\)-Loewner chains, Bloch functions and extension operators in complex Banach spaces ⋮ Loewner chains, Bloch mappings and Pfaltzgraff-Suffridge extension operators on bounded symmetric domains ⋮ Loewner chains associated with close to almost starlike mappings of order \(\alpha \) ⋮ Extension operators preserving Janowski classes of univalent functions ⋮ The Muir extension operator and Janowski univalent functions ⋮ Subclasses of biholomorphic mappings associated withg-Loewner chains on the unit ball in ℂⁿ

Cites Work

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• Loewner chains and the Roper-Suffridge extension operator
• Univalent mappings associated with the Roper-Suffridge extension operator
• Convex mappings on the unit ball of \(\mathbb C^ n\)
• Subordination chains and univalence of holomorphic mappings in C\(^n\)
• Loewner chains associated with the generalized Roper-Suffridge extension operator
• On the variational method for univalent functions
• An Extension Theorem and Subclasses of Univalent Mappings in Several Complex Variables
• Parametric Representation of Univalent Mappings in Several Complex Variables
• Über die Subordination analytischer Funktionen.
• The generalized Roper-Suffridge extension operator
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