Geometric properties of a domain with cusps

For $ngeq 4$ (even), the function $varphi_{nmathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps the unit disk $mathbb{D}$ onto a domain bounded by an epicycloid with $n-1$ cusps. In this paper, the class $mathcal{S}^*_{nmathcal{L}} = mathcal{S}^*(varphi_{nmathcal{L}})$ is studied and various inclusion relations are established with other subclasses of starlike functions. The bounds on initial coefficients is also computed. Various radii problems are also solved for the class $mathcal{S}^*_{nmathcal{L}}$.