Geometric properties of a domain with cusps

Abstract

For $n\ge 4$ (even), the function ${\phi }_{n\mathcal{L}}(z)=1+nz/(n+1)+z^n/(n+1)$ maps the unit disk $\mathbb{D}$ onto a domain bounded by an epicycloid with $n-1$ cusps. In this paper, the class ${\mathcal{S}}_{n\mathcal{L}}^{\ast }={\mathcal{S}}^{\ast }({\phi }_{n\mathcal{L}})$ 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 ${\mathcal{S}}_{n\mathcal{L}}^{\ast }$.

23 pages Comments are welcome

References in corpus (1)

• On the radius constants for classes of analytic functions