Geodesic
The sum of coefficients of bounded univalent functions
Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 728-733 
D. V. Prokhorov. The sum of coefficients of bounded univalent functions. Matematičeskie zametki, Tome 61 (1997) no. 5, pp. 728-733. http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a9/
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     author = {D. V. Prokhorov},
     title = {The sum of coefficients of bounded univalent functions},
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     volume = {61},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_5_a9/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We solve the maximal value problem for the functional $\operatorname{Re}\sum_{j=1}^ma_{k_j}$ in the class of functions $f(z)=z+a_2z^2+\dotsb$ that are holomorphic and univalent in the unit disk and satisfy the inequality $|f(z)|. We prove that the Pick functions are extremal for this problem for sufficiently large $M$ whenever the set of indices $k_1,\dots,k_m$ contains an even number.

[1] Prokhorov D. V., “Even coefficient estimates for bounded univalent functions”, Ann. Polon. Math., 58:3 (1993), 267–273 | MR | Zbl

[2] Prokhorov D. V., “Mnozhestva znachenii sistem funktsionalov v klassakh odnolistnykh funktsii”, Matem. sb., 181:12 (1990), 1659–1677

[3] Bshouty D., “A coefficient problem of Bombieri concerning univalent functions”, Proc. Amer. Math. Soc., 91:3 (1984), 383–388 | DOI | MR | Zbl