Some remarks for certain subclasses of meromorphic 1 - valent functions

B.N. Ornek

Authors

B.N. Ornek Amasya University, Merkez-Amasya, Tukey

Keywords:

Holomorphic function, Meromorphic function, Jack's lemma, Angular derivative

Abstract

In this paper, a boundary version of the Schwarz lemma for classes N(λ) is investigated. For the function f (z) = 1/z + c₁z + c₂z² + ... defined in the punctured unit disc D = { z∈ $\mathbb{C}$ : 0 < |z| < 1 } such that f (z) ∈ N(λ), we estimate a modulus of the angular derivative of f″ (z) function at the boundary point b with f ′(b) =(-1+λ)/2b². The sharpness of these inequalities is also proved.