In this paper, we give some results on $\frac{zf^{\prime }(z)}{f(z)}$ forthe certain classes of holomorphic functions in the unit disc $U=\left\{z:\left\vert z\right\vert <1\right\} $ and on $\partial U=\left\{z:\left\vert z\right\vert =1\right\} $. For the function $%f(z)=z+c_{2}z^{2}+c_{3}z^{3}+...$ defined in in the unit disc $U$ such that $%f(z)\in \mathcal{M}$, we estimate a modulus of the angular derivative $\frac{%zf^{\prime }(z)}{f(z)}$ function at the boundary point $b$ with $f^{\prime}(b)=0$. Moreover, Schwarz lemma for class $\mathcal{M}$ is given. Thesharpness of these inequalities is also proved.
@article{7545,
title = {Applications of the Jack's lemma for the holomorphic functions},
journal = {Novi Sad Journal of Mathematics},
volume = {48},
year = {2018},
language = {EN},
url = {http://dml.mathdoc.fr/item/7545}
}
ÖRNEK, Bülent Nafi; Aydınoğlu, Selin. Applications of the Jack's lemma for the holomorphic functions. Novi Sad Journal of Mathematics, Tome 48 (2018) . http://gdmltest.u-ga.fr/item/7545/