Toshiyuki SUGAWA
On the norm of pre-Schwarzian derivatives of strongly starlike functions
Abstract
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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