A Generalization of Univalent Functions with Negative Coefficients

Abstract:

      Let R_A,B(α,β,q) denote the class of functions f(z) = z(?) which are analytic and nnivalent in < 1, and satisfy the condition. Also let R_A,B(α,β,q,t) denote the class of functions (1 - t)z + tf(z), where f(z) ∈R_A,B(α,β, q) and t ∈(0, 1].Sharp results concerning representation, distortion theorems and radius of convexityfor the class R_A,B(α,β, q, t) are determined. It is shown that the class R_A,B(α,β,q, t)is closed under linear combinations. Furthermore extreme points and support points forthe class R_A,B(α,β,q, t) are also determined.