Some estimates for angular derivative at the boundary

Abstract

In this paper, we establish lower estimates for the modulus of the values of f(z) on boundary of unit disc. For the function f(z) = 1 + c1z + c2z2 +… defined in the unit disc such that f(z) ? N (?) assuming the existence of angular limit at the boundary point b, the estimations below of the modulus of angular derivative have been obtained at the boundary point b with f(b) = ?. Moreover, Schwarz lemma for class N (?) is given. The sharpness of these inequalities has been proved. © Bülent Nafi Örnek, 2017.