Some results for classes of holomorphic functions

Abstract

In this paper, a boundary version of the Schwarz lemma for classes K(α) is investigated. For the function f(z) = 1 + c₁ z + c₂ z² + ... defined in the unit disc such that f(z) ∈ K(α), we estimate a modulus of the angular derivative of f(z) function at the boundary point b with f(b) = α. Also, we shall give an estimate below | f'(b)| according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and z₀ ≠ 0. The sharpness of these inequalities is also proved.