Quasi-convex mappings of order \(\alpha\) on the unit polydisk in \(\mathbb{C}^n\)

DOI10.1216/RMJ-2010-40-5-1619zbMath1209.32006OpenAlexW2093997422MaRDI QIDQ613536

Ming-Sheng Liu, Xiaosong Liu

Publication date: 21 December 2010

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2010-40-5-1619

zbMATH Keywords

\(k\)-fold symmetricconvex function of order \(\alpha\)estimation of homogeneous expansionquasiconvex mapping of type B and order \(\alpha\)

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) Other generalizations of function theory of one complex variable (32A30)

Related Items (8)

Sharp estimates of quasi-convex mappings of type B and order \(\alpha\) ⋮ Coefficient problems of quasi-convex mappings of type B on the unit ball in complex Banach spaces ⋮ Toeplitz determinants for a class of holomorphic mappings in higher dimensions ⋮ Sharp inequalities of homogeneous expansions of almost starlike mappings of order alpha ⋮ The estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation in several complex variables ⋮ The sharp estimates of all homogeneous expansions for a class of quasi-convex mappings on the unit polydisk in \(\mathbb C^{n}\) ⋮ The coefficient inequalities for a class of holomorphic mappings in several complex variables ⋮ The sharp estimates of homogeneous expansions for the generalized class of close-to-quasi-convex mappings

Cites Work

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• Some sufficient conditions for biholomorphic convex mappings on \(B_p^n\)
• Construction of biholomorphic convex mappings on \(D_p\) in \(\mathbb{C}^n\)
• On the quasi-convex mappings on the unit polydisk in \(\mathbb C^{n}\)
• On Products of Starlike Functions
• Convexity properties of holomorphic mappings in ℂⁿ
• On some best bounds for coefficients of several subclasses of biholomorphic mappings in Cⁿ
• THE GROWTH THEOREM FOR $k$ -FOLD SYMMETRIC CONVEX MAPPINGS
• On the theory of univalent functions

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