Pre-Schwarzian norm estimate and characterization of certain harmonic mappings

Abstract

In this article, we consider certain class of harmonic mappings defined in the unit disk $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}.$ Then we obtain pre-Schwarzian norm estimate of functions in the class. Next, we show that functions in the considered class are univalent and close-to-convex. Moreover, we discuss some growth and distortion theorems for associated analytic and co-analytic parts of harmonic mappings in the class. At last, we present coefficient estimate for the analytic part.