Subclass of starlike functions associated with a limacon

Abstract

Let S*LC represent a new subclass of analytic functions f defined in the open unit disk in the complex plane such that zf’(z)f(z) lies in the interior of the domain bounded by the limacon given by the equation (4x2+4y2−8x−5)2+8(4x2+4y2−12x−3)=0. In this paper, we investigate the geometric properties of functions in this class.