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Bull. Korean Math. Soc. 2014; 51(3): 803-812

Printed May 31, 2014

https://doi.org/10.4134/BKMS.2014.51.3.803

Copyright © The Korean Mathematical Society.

Harmonic mappings related to functions with bounded boundary rotation and norm of the pre-Schwarzian derivative

Stanis{\l}awa Kanas and Dominika Klimek-Sm\c{e}t

University of Rzeszow, Maria Curie-Sk{\l}odowska University

Abstract

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Let $\mathcal{S}^0_\mathcal{H}$ be the class of normalized univalent harmonic mappings in the unit disk. A subclass $\mathcal{V}^{\mathcal{H}}(k)$ of $\mathcal{S}^0_\mathcal{H}$, whose analytic part is function with bounded boundary rotation, is introduced. Some bounds for functionals, specially harmonic pre-Schwarzian derivative, described in $\mathcal{V}^{\mathcal{H}}(k)$ are given.

Keywords: univalent harmonic mappings, functions with bounded boundary rotation

MSC numbers: Primary 31A05; Secondary 30C45

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