Certain classes of univalent functions with negative coefficients

Abstract

The subclasses S*(α, β) and C*(α, β) of T, the class of analytic and univalent functions of the form have been considered. Sharp results concerning coefficients, distortion of functions belonging to S*(α, β) and C*(α, β) are determined along with a representation formula for the functions in S*(α, β). Furthermore, it is shown that the classes S*(α, β) and C*(α,.β) are closed under arithmetic mean and convex linear combinations.