On Certain Classes of Univalent Functions with Negative and Missing Coefficients

摘要

Let p~*(A,B,k,a,β) be the class of functions f(z)=a_1-sum from n=k to ∞(|a_n|Z^n) (a_1>0,k≥2) regular and univalent in the unit disc U={z:|z|<1}and satis-fying where and We denote by P_o(A,B,k, α,β,z_o) and p_1(A,k,α,β,z_o), two suoclasses of p~*(A,B,k,α,β), consisting of the functions which satisfy f(z_n)=z_n and f′(z_n)=1,respectively, here In this paper we obtain ooefficient estimates,distortion and closure theorems and radius of convexity of order p (0≤ρ<1)for the classes P_o(A,B,k, α,β,z_0) and P_1(A,B,k,α,β,z_o).