On an application of Jack's lemma, starlikeness and \(k\)-fold symmetry in \(\mathbb{C}^n\)

DOI10.1007/s11785-022-01271-2zbMath1504.32010OpenAlexW4293698312WikidataQ114221743 ScholiaQ114221743MaRDI QIDQ2080172

Piotr Liczberski, Renata Długosz

Publication date: 7 October 2022

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

Full work available at URL: https://doi.org/10.1007/s11785-022-01271-2

zbMATH Keywords

star-like mappings\(n\)-dimensional version of Jack's lemmalocally biholomorphic mappings in \(\mathbb{C}^n\)

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)

Cites Work

• Relations among starlikeness, convexity and \(k\)-fold symmetry of locally biholomorphic mappings in \(\mathbb{C}^n\)
• On a certain univalent mapping
• The growth and 1/4-theorems for starlike mappings in \(\mathbb{C}^ n\)
• Close-to-starlike holomorphic functions of several variables
• Applications of a decomposition of holomorphic mappings in \(\mathbb C^n\) with respect to a cyclic group
• The principle of subordination applied to functions of several variables
• Starlike and convex mappings in several complex variables
• On a new proof and an extension of Jack's lemma
• Julius and Julia: Mastering the Art of the Schwarz Lemma
• k-FOLD SYMMETRICAL MAPPINGS AND LOEWNER CHAINS
• A uniqueness theorem of Cartan–Gutzmer type for holomorphic mappings in Cⁿ
• A starlikeness criterion for holomorphic mappings in C ⁿ
• Functions Starlike and Convex of Order α
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