  Let $\mathcal{G}(\alpha)$ denote the family of functions $ f(z)$ in the open
unit disk $\mathbb D :=\{z\in\mathbb{C}: |z|<1\}$ that satisfy $ f(0)=0=
f'(0)=1$ and \[\Re \left(1+ \dfrac{z f''(z)}{ f'(z)}\right)<1+\dfrac{\alpha}{2}
, \quad z\in \mathbb D.\] We determine the disks $|z|<\rho_n$ 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.
