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

We have introduced a new subclass of harmonic univalent functions denoted by T_H^k(α, γ, β) , which is a harmonic analogue to the functions class W_β(α, γ) (see [4]). It is observed that there is an analytic bridge between two classes T_H^k(α, γ, β) and W_β(α, γ) . 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.