On the precise growth, covering, and distortion theorems for normalized biholomorphic mappings

DOI10.1016/j.jmaa.2004.02.052zbMath1052.58013OpenAlexW2093818523MaRDI QIDQ596734

Xiaosong Liu, Tai Shun Liu

Publication date: 10 August 2004

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.2004.02.052

zbMATH Keywords

complex Banach spacebiholomorphic mappingquasi-convex mappingstarlike mappingstarlike mapping of order \(\alpha\)convex mappingcovering resultdistortion resultgrowth result

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) Holomorphic maps on manifolds (58C10) Questions of holomorphy and infinite-dimensional manifolds (58B12)

Related Items (11)

Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation ⋮ Sharp distortion theorems for a class of biholomorphic mappings in several complex variables ⋮ Sharp growth and distortion theorems for a subclass of biholomorphic mappings ⋮ The refined Schwarz-Pick estimates for positive real part holomorphic functions in several complex variables ⋮ Sharp growth theorems and coefficient bounds for starlike mappings in several complex variables ⋮ On the generalized class of close-to-convex mappings ⋮ On a subclass of close-to-convex mappings ⋮ The sharp estimates of all homogeneous expansions for a class of quasi-convex mappings on the unit polydisk in \(\mathbb C^{n}\) ⋮ A refinement of the coefficient inequalities for a subclass of starlike mappings in several complex variables ⋮ Criteria for biholomorphic convex mappings on the unit ball in Hilbert spaces ⋮ Sharp distortion theorems for a subclass of close-to-convex mappings

Cites Work

• The growth and 1/4-theorems for starlike mappings in \(\mathbb{C}^ n\)
• The growth theorem for starlike mappings on bounded starlike circular domains
• Distortion theorems for biholomorphic convex mappings on bounded convex circular domains
• Convex mappings on the unit ball of \(\mathbb C^ n\)
• On growth and covering theorems of quasi-convex mappings in the unit ball of a complex Banach space
• Nonlinear semigroups and evolution equations
• Starlike and convex maps in Banach spaces
• Growth and Distortion Results for Convex Mappings in Infinite Dimensional Spaces
• Convexity properties of holomorphic mappings in ℂⁿ
• A Distortion Theorem for Biholomorphic Mappings in ℂ 2
• THE GROWTH THEOREM FOR $k$ -FOLD SYMMETRIC CONVEX MAPPINGS
• Coefficient Estimates for Univalent Functions
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