Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 127-130
Citer cet article
V. A. Baranova. A bound for the coefficient $c_4$ for one-sheeted functions in terms of $|c_2|$. Matematičeskie zametki, Tome 12 (1972) no. 2, pp. 127-130. http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a1/
@article{MZM_1972_12_2_a1,
author = {V. A. Baranova},
title = {A bound for the coefficient $c_4$ for one-sheeted functions in terms of $|c_2|$},
journal = {Matemati\v{c}eskie zametki},
pages = {127--130},
year = {1972},
volume = {12},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a1/}
}
TY - JOUR
AU - V. A. Baranova
TI - A bound for the coefficient $c_4$ for one-sheeted functions in terms of $|c_2|$
JO - Matematičeskie zametki
PY - 1972
SP - 127
EP - 130
VL - 12
IS - 2
UR - http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a1/
LA - ru
ID - MZM_1972_12_2_a1
ER -
%0 Journal Article
%A V. A. Baranova
%T A bound for the coefficient $c_4$ for one-sheeted functions in terms of $|c_2|$
%J Matematičeskie zametki
%D 1972
%P 127-130
%V 12
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1972_12_2_a1/
%G ru
%F MZM_1972_12_2_a1
In the class $S$ of functions $f(z)=z+\sum_{k=2}^\infty c_kz^k$ which are regular and single-sheeted in the circle $|z|<1$, the bound for $|c_4|$ in terms of $|c_2|$, obtained by Al'fors, is improved. The crudest bound $|c_4|\leqslant4/15(11+|c_2|)$ is better than that of Al'fors: $|c_4|\leqslant(4/\sqrt{15})\sqrt{11+|c_2|^2}$.
