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Applications of the Jack's Lemma for the Meromorphic Functions at the Boundary
(SOC PARANAENSE MATEMATICA, 2020) Akyel, Tugba; Ornek, Bulent Nafi
In this paper, a boundary version of the Schwarz lemma for classes N(beta) is investigated. For the function f(z) = 1/z + a(0) + a(1)z + a(2) z(2) +... defined in the punctured disc E such that f(z) is an element of N(beta), we estimate a modulus of the angular derivative of the function zf'(z)/f(z) at the boundary point c with cf '(c)/f(c) = 1-2 beta/beta. Moreover, Schwarz lemma for class N(beta) is given.
ESTIMATES FOR A CERTAIN SUBCLASS OF HOLOMORPHIC FUNCTIONS
(KOREAN SOC MATHEMATICAL EDUCATION, 2019) Ornek, Bulent Nafi; Akyel, Tugba
In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to N(alpha) is investigated. For the function f(z) = z + c(2)z(2) + c(3)z(3) + ... which is defined in the unit disc where f(z) is an element of N(alpha), we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with f (b) = 1/b integral(b)(0) f(t)dt. The sharpness of these inequalities is also proved.