Partial sums and geometric properties of certain unified family of harmonic mappings

Abstract

We have introduced a new subclass of harmonic univalent functions denoted by $T_H^k(\alpha,\gamma,\beta)$, which is a harmonic analogue to the functions class $\mathcal W_\beta(\alpha,\gamma)$ (see \cite{ali1}). It is observed that there is an analytic bridge between two classes $T_H^k(\alpha,\gamma,\beta)$ and $\mathcal W_\beta(\alpha,\gamma)$. Various geometric properties such as sharp coefficient bounds, growth theorem, sufficient condition, invariance property under convolution and convex combination, radius of starlikeness, convexity and close-to-convexity of the partial sums of functions are discussed.