Yusuke OKUYAMA

### Abstract

For a constant $\beta\in (-\pi /2,\pi /2)$, a normalized analytic function $f(z)=z+a_2z^2+a_3z^3+\cdots$ on the unit disk is said to be $\beta$ -spiral-like if $\Re (\frac{zf'(z)}{e^{i\beta}f(z)})>0$ for any point $z$ in the unit disk. In this paper, for such a function $f$, we shall present the optimal estimate of the norm of $f''/f'$.

submission: October 30, 1998
revised: September 1, 1999
revised: December 26, 1999

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