Geodesic
Coefficients of univalent functions which assume no pair of values $W$ and $-W$
Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 3-14

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In this paper we study the behavior of the coefficients of functions $\varphi(z)=1+\sum_{k=1}^\infty b_kz^k$, univalent in the disk $|z|1$ and assuming there are no pair of values $W$ and $-W$. In particular, we establish the asymptotic behavior of $b_n$ ($n\to\infty$); for the coefficients we obtain the estimate $|b_n|2,34\exp\{1/4n\}$ ($n=2,3,\dots$) and for each function of the class indicated we prove, subject to a certain condition, the relationship $||b_{n+1}|-|b_n||=O(n^{-1/2})$. 
@article{MZM_1972_11_1_a0,
     author = {A. Z. Grinshpan},
     title = {Coefficients of univalent functions which assume no pair of values $W$ and $-W$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a0/}
}
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A. Z. Grinshpan. Coefficients of univalent functions which assume no pair of values $W$ and $-W$. Matematičeskie zametki, Tome 11 (1972) no. 1, pp. 3-14. http://geodesic.mathdoc.fr/item/MZM_1972_11_1_a0/