Let S * lim represent a subclass of analytic functions f defined in the unit disk such that z f ′ (z) f (z) lies in the interior of the region bounded by the limacon which is given by the equation (u − 1) 2 + v 2 − 1 4 2 − 2 u − 1 + 1 2 2 + v 2 = 0. For this class, we obtain the structural formula, inclusion results and some radii problems for subclasses of starlike functions. Furthermore, we obtain sufficient conditions and coefficient bounds for this class of functions.