  We introduce and study a class of starlike functions defined by
\begin{equation*} \mathscr{S}^*_\wp:=\left\{f\in\mathcal{A}:
\frac{zf'(z)}{f(z)}\prec 1+ze^z=:\wp(z)\right\}, \end{equation*} where $\wp$
maps the unit disk onto a cardioid domain. We find the radius of convexity of
$\wp(z)$ and establish the inclusion relations between the class $
\mathscr{S}^*_\wp$ and some well-known classes. Further we derive sharp radius
constants and coefficient related results for the class $ \mathscr{S}^*_\wp$.
