Displaying similar documents to “Coefficient estimates and Landau-Bloch's constant for planar harmonic mappings.”

On a result by Clunie and Sheil-Small

Dariusz Partyka, Ken-ichi Sakan (2012)

Annales UMCS, Mathematica

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In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping F in the unit disk D, if F(D) is a convex domain, then the inequality |G(z2)− G(z1)| < |H(z2) − H(z1)| holds for all distinct points z1, z2∈ D. Here H and G are holomorphic mappings in D determined by F = H + Ḡ, up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain Ω in ℂ and improve it...

Some Growth and Distortion Theorems for Close-to-Convex Harmonic Functions in the Unit Disc

Polatoğlu, Yaşar (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 30C45, 30C55 One of the most important questions in the study of the classes of such functions is related to bounds on the modulus of functions (growth) or modulus of the derivative (distortion). The aim of this paper is to give the growth and distortion theorems for the close-to-convex harmonic functions in the open unit disc D.