A rotation theorem in the class of bounded univalent functions

V. V. Goryainov

Institute of Applied Mathematics and Mechanics, Academy of Sciences of UkSSR

Abstract: Let $S_M$, $M>1$, be the class of functions $f(z)$ which are regular and univalent in the disk $|z|<1$ and satisfy the conditions $f(0)=0$, $f'(0)=1$, $|f(z)|<M$. In the present note we will obtain an exact estimate for the argument of the derivative of a function of the class $S_M$.

UDC: 517.54

Received: 30.10.1974

 English version: Mathematical Notes, 1975, 18:5, 967–971

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