Geodesic
$\alpha$-Convexity of schlicht functions
Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 227-232

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Upper and lower bounds are obtained for the radius of $\alpha$-convexity, $R_\alpha$, of the schlicht within $|z|1$ functions $g(z)$, $g(0)=0$, and $g'(0)=1$, for $\alpha$ values ranging from 0 to $0.313\ldots$. The exact value of $R_\alpha$ is determined for $0,313\ldots\leqslant\alpha1$. The results constitute the solution to a problem recently posed by the Roumanian mathematician P. T. Mocanu [1]. 
@article{MZM_1972_11_2_a12,
     author = {V. V. Chernikov},
     title = {$\alpha${-Convexity} of schlicht functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {227--232},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a12/}
}
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V. V. Chernikov. $\alpha$-Convexity of schlicht functions. Matematičeskie zametki, Tome 11 (1972) no. 2, pp. 227-232. http://geodesic.mathdoc.fr/item/MZM_1972_11_2_a12/