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

We consider a version of the boundary Schwarz Lemma on a certain class which is denoted by K(α). For the function f (z) = z + c₂ z² + c₃ z³ + … defined in the unit disc E such that the function f(z) belongs to the class K(α), we estimate from below the modulus of the angular derivative of the function $zf′(z)f(z)$ at the boundary point b with $bf′(b)f(b)=11+α$⁠. Moreover, we get Schwarz Lemma for the class K(α). We also investigate some inequalities obtained in terms of sharpness.