Geodesic
The radius of almost convexity of order $\alpha$ in the class of univalent functions
Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 105-112.

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In this paper the radius of almost convexity of order $\alpha$ in the class of functions $f(z)=z+a_2z^2+\dots$ analytic and univalent in $|z|1$ is found. The solution to a problem of A. Renyi is given in this connection. 
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     author = {P. I. Sizhuk},
     title = {The radius of almost convexity of order $\alpha$ in the class of univalent functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {105--112},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a10/}
}
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P. I. Sizhuk. The radius of almost convexity of order $\alpha$ in the class of univalent functions. Matematičeskie zametki, Tome 20 (1976) no. 1, pp. 105-112. http://geodesic.mathdoc.fr/item/MZM_1976_20_1_a10/