Norm of the pre-Schwarzian derivative, Bloch's constant and coefficient bounds in some classes of harmonic mappings

Abstract

The aim of the paper is a study of a family of sense-preserving complex valued harmonic functions f that are normalized in the open unit disk, and such that its analytic part is convex in one direction. We prove the univalence and establish estimates on pre-Schwarzian derivative and the Bloch constant for co-analytic part of harmonic mapping. The bounds of the coefficients of co-analytic part are also given.