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HARMONIC MAPPINGS RELATED TO FUNCTIONS WITH BOUNDED BOUNDARY ROTATION AND NORM OF THE PRE-SCHWARZIAN DERIVATIVE

  • Kanas, Stanis lawa (Stanis lawa Kanas University of Rzeszow) ;
  • Klimek-Smet, Dominika (Maria Curie-Sk lodowska University)
  • Received : 2013.04.16
  • Published : 2014.05.31

Abstract

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

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