Starlikness Associated with Limacon

Abstract

Let S_{lim}^{∗} represent a subclass of analytic functions f defined in the unit disk such that ((zf′(z))/(f(z))) lies in the interior of the region bounded by the limacon which is given by the equation [(u-1)²+v²-(1/4)]²-2[(u-1+(1/2))²+v²]=0. For this class, we obtain the structural formula, inclusion results and some radii problems for subclasses of starlike functions. We also find radii problems for the ratios of certain analytic functions. Furthermore, we obtain sufficient conditions for this class of functions.