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

  • I. M. Kotsur
  • M. F. Kotsur

Abstract

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.
Published
25.07.1996
How to Cite
KotsurI. M., and KotsurM. F. “On the Radii of Convexity and Starlikeness for Some Special Classes of Analytic Functions in a Disk”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 48, no. 7, July 1996, pp. 954-8, https://umj.imath.kiev.ua/index.php/umj/article/view/5268.
Section
Research articles