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Sharp starlikeness conditions for analytic functions with bounded derivative
Published online by Cambridge University Press: 09 April 2009
Abstract
We develop sharp conditions for various types of starlikeness for functions analytic in the unit disk with bounded derivatives. We also describe the precise range {zf′(z)/f(z): z ∈ D, f ∈ }, where f ∈
means f (0) = 0, f′(0) = 1, and |f′(z) - 1 |< ≦ λ in the unit disc D, and draw some cnoslusions from that.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 69 , Issue 3 , December 2000 , pp. 303 - 315
- Copyright
- Copyright © Australian Mathematical Society 2000
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