Geometric properties of a domain with cusps

For n\geq 4 (even), the function \varphi_{n\mathcal{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}^*_{n\mathcal{L}} = \mathcal{S}^*(\varphi_{n\mathcal{L}}) is studied and various inclusion relations are established with other subclasses of starlike functions. The bounds on initial coefficients is... Show more