Geometric subfamily of functions convex in some direction and Blaschke products

Consider the family of locally univalent analytic functions $h$ in the unit disk $\mathrm{\mid }z\mathrm{\mid }<1$ with the normalization $h(0)=0$, $h^{\mathrm{\prime }}(0)=1$ and satisfying the condition {\real} \left( \frac{z h''(z)}{αh'(z)}\right) <\frac{1}{2} ~ for $z\in \ID$, where $0<\alpha \le 1$. The aim of this article is to show that this family has several elegant properties such as involving Blaschke products, Schwarzian derivative and univalent harmonic mappings.