2019
Том 71
№ 8

All Issues

Kotsur M. F.

Articles: 1
Article (Russian)

On the radii of convexity and starlikeness for some special classes of analytic functions in a disk

Kotsur I. M., Kotsur M. F.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 954-958

We introduce the class O α, 0≤α≤1, of functions w=ƒ(z), ƒ(0)=0, ƒ′(0)=0,..., ƒ (0) (n−1) =0, f (n)(0)=(n-l)! analytic in the disk |z|<1 and satisfying the condition $$\operatorname{Re} \left( {\frac{{1 - 2z^n \cos \Theta + z^{2n} }}{{z^{n - 1} }}f'(z)} \right) > \alpha , 0 \leqslant \Theta \leqslant \pi , n = 1,2,3,... .$$ We establish the radius of convexity in the class Oα and the radius of starlikeness in the class Uα of functions σ(z)=zƒ′(z), ƒ(z)⊂O α.