Extension of convex mappings of order \(\alpha \) of the unit disk in \(\mathbb C\) to convex mappings of the unit ball in \(\mathbb C^n\)

DOI10.1016/J.JMAA.2009.03.016zbMath1168.32014OpenAlexW1985509773MaRDI QIDQ1023033

Jerry R. jun. Muir

Publication date: 10 June 2009

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.2009.03.016

zbMATH Keywords

extension operatorconvex mappingorder \(\alpha\)

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Holomorphic functions of several complex variables (32A10)

Related Items (4)

Convex mappings associated with the Roper-Suffridge extension operator ⋮ The roles played by order of convexity or starlikeness and the Bloch condition in the extension of mappings from the disk to the ball ⋮ Analytic and geometric properties associated with some extension operators ⋮ Extension operators preserving Janowski classes of univalent functions

Cites Work

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• A modification of the Roper-Suffridge extension operator
• Locally convex functions and the Schwarzian derivative
• Extension operators for locally univalent mappings
• Loewner chains and the Roper-Suffridge extension operator
• Convex mappings on the unit ball of \(\mathbb C^ n\)
• A class of Loewner chain preserving extension operators
• Starlike and convex mappings in several complex variables
• Convex Hulls and Extreme Points of Families of Starlike and Convex Mappings

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