Estimates for derivatives of holomorphic functions in a hyperbolic domain |
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Authors: | Jian-Lin Li |
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Institution: | College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, PR China |
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Abstract: | Let f(z) be a holomorphic function in a hyperbolic domain Ω. For 2?n?8, the sharp estimate of |f(n)(z)/f′(z)| associated with the Poincaré density λΩ(z) and the radius of convexity ρΩc(z) at z∈Ω is established for f(z) univalent or convex in each Δc(z) and z∈Ω. The detailed equality condition of the estimate is given. Further application of the results to the Avkhadiev-Wirths conjecture is also discussed. |
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Keywords: | Univalent function Convex function Hyperbolic domain Poincaré density Radii of univalency and convexity |
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