The second and third Hankel determinants for certain convex subclass of functions

Let $\mathcal{A}$ denote the class of analytic functions such that $f(0)=0$ and $f^{\mathrm{\prime }}(0)=1$ in the unit disk $\mathbb{D}:=\{z\in \mathbb{C}:\mathrm{\mid }z\mathrm{\mid }<1\}\mathrm{.}$ In the present paper, we consider $\mathcal{C}(\phi ):=\{f\in \mathcal{A}:1+z{f}^{\mathrm{\prime }\mathrm{\prime }}(z)\mathrm{/}{f}^{\mathrm{\prime }}(z)\prec \phi (z):=(1+z\mathrm{/}2{)}^2\}$, as subclass of convex functions and compute the sharp second and third Hankel determinants for functions in $\mathcal{C}(\phi )$.