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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2009 Volume 371, Pages 171–175 (Mi znsl3552)

Short communications

On distortion theorems for typically real functions

E. G. Goluzina

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg

Abstract: The author's investigation in the class $T$ of typically real functions $f(z)$ in the disk $|z|<1$ are prolonged. The region of values of $f'(z_1)$ in the class of functions $f\in T$ with fixed values $f(z_1)$ and $f(r_j)$ $(j=1,2)$ is determined. Here $|z_1|<1$, $\operatorname{Im}z_1\ne0$, $0<r_j<1$ $(j=1,2)$. Bibl. – 4 titles.

Key words and phrases: typically real function, distortion theorems, region of values.

UDC: 517.54

Received: 12.11.2009


 English version:
Journal of Mathematical Sciences (New York), 2010, 166:2, 222–224

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© Steklov Math. Inst. of RAS, 2024