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

Authors

  • 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 Re(12zncosΘ+z2nzn1f(z))>α,0 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

Issue

Section

Research articles

How to Cite

Kotsur, I. M., and M. F. Kotsur. “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.