Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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: $|c_4|\leqslant(4/\sqrt{15})\sqrt{11+|c_2|^2}$. 
@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/}
}
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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/