On a subclass of close-to-convex harmonic mappings

For $\alpha >-1$ and $\beta >0,$ let $$\mathcal{B}$_{$\mathcal{H}$}^0(\alpha, \beta)$denotetheclassofsensepreservingharmonicmappings$f=h+\overline{g}$intheopenunitdisk$$\mathbb{D}$$satisfying$|zh’‘(z)+\alpha(h’(z)-1)|\leq \beta-|zg’‘(z)+\alpha g’(z)|.$ First, we establish that each function belonging to this class is close-to-convex in the open unit disk if $\beta \in (0,1+\alpha ]$. Next, we obtain coefficient bounds, growth estimates and convolution properties. We end the paper with applications and will construct harmonic univalent polynomials belonging to this class.