HARMONIC MAPPINGS RELATED TO FUNCTIONS WITH BOUNDED BOUNDARY ROTATION AND NORM OF THE PRE-SCHWARZIAN DERIVATIVE
HARMONIC MAPPINGS RELATED TO FUNCTIONS WITH BOUNDED BOUNDARY ROTATION AND NORM OF THE PRE-SCHWARZIAN DERIVATIVE
Let <TEX>${\mathcal{S}}^0_{\mathcal{H}}$</TEX> be the class of normalized univalent harmonic mappings in the unit disk. A subclass <TEX>${\mathcal{V}}^{\mathcal{H}}(k)$</TEX> of <TEX>${\mathcal{S}}^0_{\mathcal{H}}$</TEX>, whose analytic part is function with bounded boundary rotation, is introduced. Some bounds for functionals, specially harmonic pre-Schwarzian derivative, described in <TEX>${\mathcal{V}}^{\mathcal{H}}(k)$</TEX> are given.