Toshiyuki SUGAWA

On the norm of pre-Schwarzian derivatives of strongly starlike functions


For a constant $ \alpha\in(0,1], $ a normalized analytic function $ f(z)=z+a_2z^2+\cdots $ on the unit disk is said to be strongly starlike of order $ \alpha $ if $ |\text{arg}zf'(z)/f(z)| <\alpha \pi/2 $ for any point $ z $ in the unit disk. In this note, we shall present an optimal but not explicit esitimate of the norm of $ f''/f', $ for such a function $ f. $ And we provide a sufficiently good esitimate for the optimal constants. We also refer to the related topics.

submission: August 5, 1997

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