Study of subclasses of starlike and convex functions

Abstract

In this article, we introduce new subclasses of starlike and convex functions by using a new differential operator defined in the open unit disk U. We study the geometric properties of such subclasses of starlike and convex functions. The vertices, co-vertices, coordinates of foci and equation of directrix are discussed in detail. Finally, we investigate various convolution properties of these subclasses.