[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c180157

APPLICATIONS OF JACK'S LEMMA FOR CERTAIN SUBCLASSES OF HOLOMORPHIC FUNCTIONS ON THE UNIT DISC

Catal, Batuhan (Department of Mathematics Amasya University)
ornek, Bulent Nafi (Department of Computer Engineering Amasya University)

Publication Information

Communications of the Korean Mathematical Society / v.34, no.2, 2019 , pp. 543-555 More about this Journal

Abstract

In this paper, we give some results on ${\frac{zf^{\prime}(z)}{f(z)}}$ for the certain classes of holomorphic functions in the unit disc $$E=\{z:{\mid}z{\mid}$ < $1\}$$ and on ${\partial}E=\{z:{\mid}z{\mid}=1\}$ . For the function $f(z)=z^2+c_3z^3+c_4z^4+{\cdots}$ defined in the unit disc E such that $f(z){\in}{\mathcal{A}}_{\alpha}$ , we estimate a modulus of the angular derivative of ${\frac{zf^{\prime}(z)}{f(z)}}$ function at the boundary point b with ${\frac{bf^{\prime}(b)}{f(b)}}=1+{\alpha}$ . Moreover, Schwarz lemma for class ${\mathcal{A}}_{\alpha}$ is given. The sharpness of these inequalities is also proved.

Keywords

Schwarz lemma; Jack's lemma; angular limit;

Citations & Related Records

Times Cited By KSCI : 4 (Citation Analysis)

Reference
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