Some results for classes of holomorphic functions

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Bulent Nafi Ornek
Batuhan Catal

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.

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How to Cite
Ornek, B. N., & Catal, B. (2018). Some results for classes of holomorphic functions. Gulf Journal of Mathematics, 6(1). https://doi.org/10.56947/gjom.v6i1.123
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