Geometric properties of a domain with cusps

For n ≥ 4 (even), the function φnL(z) = 1 + nz/(n+ 1) + z/(n+ 1) maps the unit disk D onto a domain bounded by an epicycloid with n−1 cusps. In this paper, the class S∗ nL = S(φnL) 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 S∗ nL.

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