Some results for a certain class of holomorphic functions at the boundary of the unit disc

Abstract

We consider a version of the boundary Schwarz Lemma on a certain class which is denoted by K(alpha). For the function f (z) = z + c(2)z(2) + c(3)z(3) + ... defined in the unit disc E such that the function f (z) belongs to the class K(alpha), we estimate from below the modulus of the angular derivative of the function zf'(z)/f(z) at the boundary point b with bf'(b)/f(b) = 1/1+alpha .Moreover, we get Schwarz Lemma for the class K(alpha). We also investigate some inequalities obtained in terms of sharpness.