APPLICATIONS OF JACK'S LEMMA FOR CERTAIN SUBCLASSES OF HOLOMORPHIC FUNCTIONS ON THE UNIT DISC

摘要

In this paper, we give some results on zf'(z)/f(z) for the certain classes of holomorphic functions in the unit disc E = {z : |z| < 1} and on δE = {z : |z| = 1}. For the function f(z) = z~2 + c3z~3 + c4z~4 +... defined in the unit disc E such that f(z) ∈ Aα, we estimate a modulus of the angular derivative of zf'(z)/f(z) function at the boundary point b with bf'(b)/ f(b) = 1 + α. Moreover, Schwarz lemma for class Aα is given. The sharpness of these inequalities is also proved.