Toshiyuki SUGAWA

### 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

dvi file34444 bytes
PDF file185204 bytes

Back