Geodesic
A geometric property of functions starlike of order $\alpha$
Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 287-293 
D. V. Prokhorov. A geometric property of functions starlike of order $\alpha$. Matematičeskie zametki, Tome 10 (1971) no. 3, pp. 287-293. http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a5/
@article{MZM_1971_10_3_a5,
     author = {D. V. Prokhorov},
     title = {A geometric property of functions starlike of order~$\alpha$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {287--293},
     year = {1971},
     volume = {10},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_3_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We determined the maximum radius $\delta_\alpha(r)$ of the disk $\Omega_r$, possessing the property that every function $f(z)$, starlike of order $\alpha$, is starlike in $|z| with respect to any point of $\Omega_r$. The problem is reduced to that of finding the minimum of a certain functional for which extremal function is determined.