On the radii of convexity and starlikeness for some special classes of analytic functions in a disk
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(1−2zncosΘ+z2nzn−1f′(z))>α,0⩽Θ⩽π,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
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.
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Section
Research articles