$\alpha$-Convexity of schlicht functions

V. V. Chernikov

Tomsk State University

Abstract: 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].

UDC: 517.5

Received: 11.02.1971

 English version: Mathematical Notes, 1972, 11:2, 141–144

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