Abstract

The class S*(b) of starlike functions of complex order b was introduced and studied by M.K. Aouf and M.A. Nasr. The authors using the Ruscheweyh derivatives introduce the class K(b) of functions close-to-convex of complex order b, b≠0 and its generalization, the classes Kn(b) where n is a nonnegative integer. Here S*(b)⊂K(b)=K0(b). Sharp coefficient bounds are determined for Kn(b) as well as several sufficient conditions for functions to belong to Kn(b). The authors also obtain some distortion and covering theorems for Kn(b) and determine the radius of the largest disk in which every f∈Kn(b) belongs to Kn(1). All results are sharp.