Starlike, convex and close-to-convex functions of complex order

Abstract

In this paper we introduce two classes P $(lambda, b)$ and R $(lambda, b)$ (b a complex number with Re(b) > 0) of functions which are analytic in the unit disc. We obtain coefficient estimates for functions in these classes and radii of close-to-convexity, starlikeness and convexity. Further, applications in the fractional calculus are given for functions in P $(lambda, b)$ and R$(lambda, b)$.