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http://dx.doi.org/10.5666/KMJ.2020.60.3.507

Applications of the Schwarz Lemma and Jack's Lemma for the Holomorphic Functions  

Ornek, Bulent Nafi (Department of Computer Engineering, Amasya University)
Catal, Batuhan (Department of Mathematics, Amasya University)
Publication Information
Kyungpook Mathematical Journal / v.60, no.3, 2020 , pp. 507-518 More about this Journal
Abstract
We consider a boundary version of the Schwarz Lemma on a certain class of functions which is denoted by 𝒩. For the function f(z) = z + a2z2 + a3z3 + … which is defined in the unit disc D such that the function f(z) belongs to the class 𝒩, we estimate from below the modulus of the angular derivative of the function ${\frac{f{^{\prime}^{\prime}}(z)}{f(z)}}$ at the boundary point c with f'(c) = 0. The sharpness of these inequalities is also proved.
Keywords
holomorphic function; the Schwarz lemma on the boundary; Jack's lemma; angular derivative;
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Times Cited By KSCI : 4  (Citation Analysis)
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