Radii for sections of functions convex in one direction

Let $\mathcal{G}(\alpha )$ denote the family of functions $f(z)$ in the open unit disk $\mathbb{D}:=\{z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1\}$ that satisfy $f(0)=0=f^{\mathrm{\prime }}(0)=1$ and $$\mathrm{\Re }(1+{\displaystyle \frac{z{f}^{\mathrm{\prime }\mathrm{\prime }}(z)}{f^{\mathrm{\prime }}(z)}})<1+{\displaystyle \frac{\alpha }{2}},z\in \mathbb{D}\mathrm{.}$$ We determine the disks $\mathrm{\mid }z\mathrm{\mid }<{\rho }_n$ in which sections $s_n(z;f)$ of $f(z)$ are convex, starlike, and close-to-convex of order $\beta (0\le \beta <1)$. Further, we obtain certain inequalities of sections in the considered class of functions.