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A SHARP SCHWARZ LEMMA AT THE BOUNDARY
Tuğba AKYEL,Bülent Nafi ÖRNEK 한국수학교육학회 2015 純粹 및 應用數學 Vol.22 No.3
In this paper, a boundary version of Schwarz lemma is investigated. For the function holomorphic f(z)=a+c_{p}z^{p}+c_{p+1}z^{p+1}+... defined in the unit disc satisfying |f(z)-1|<1, where 0 < a < 2, we estimate a module of angular
AN IMPROVED LOWER BOUND FOR SCHWARZ LEMMA AT THE BOUNDARY
Bülent Nafi ÖRNEK,Tuğba AKYEL 한국수학교육학회 2016 純粹 및 應用數學 Vol.23 No.1
In this paper, a boundary version of the Schwarz lemma for the holomrophic function satisfying f(a)=b, |a|<1, b∈ℂ and ℜf(z)>α, 0≤α<|b| for |z|<1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with ℜf(c)=α. The sharpness of these inequalities is also proved.
Estimates for a Certain Subclass of Holomorphic Functions
BÜLENT NAFI ÖRNEK,TUĞBA AKYEL 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.2
In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to N(α) is investigated. For the function f(z) = z + c2z2 + c3z3 + ... which is defined in the unit disc where f(z) ∈ N(α), we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with f(b) = 1 b b ∫ 0 f(t)dt. The sharpness of these inequalities is also proved.