$\alpha$-Convexity of schlicht functions

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 $0,313\ldots\leqslant\alpha<1$. The results constitute the solution to a problem recently posed by the Roumanian mathematician P. T. Mocanu [1].