Applications of Jack’s Lemma for the holomorphic functions

Abstract

In this paper, we give some results on (Formula presented) for certain classes of holomorphic functions on the unit disc U = {z: |z| < 1} and on ?U = {z: |z| = 1}. For the function f(z) = z+c 2 z 2 +c 3 z 3 +… defined on the unit disc U such that f ? M, we estimate a modulus of the angular derivative (Formula presented) function at the boundary point b with f ? (b) = 0. Moreover, Schwarz lemma for the class M is given. The sharpness of these inequalities is also proved. © 2018, Institute of Mathematics. All rights reserved.