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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2010 Volume 382, Pages 5–14 (Mi znsl3856)

This article is cited in 1 paper

On the region of values of the system $\{c_2,c_3,f(z_1),f'(z_1)\}$ in the class of typically real finctions

E. G. Goluzina

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

Abstract: Investigations in the well-known class $T$ of typically real functions $f(z)$ in the disk $U=\{z\colon|z|<1\}$ are continued. The region of values of the system $\{c_2,c_3,f(z_1),f'(z_1)\}$ in the class $T$ is investigated. The region of values of $f'(z_1)$ in the class of functions $f\in T$ with fixed values $c_2, c_3$ and $f(z_1)$ is determined. Bibl. 10 titles.

Key words and phrases: typically real function, distortion theorem.

UDC: 517.54

Received: 16.09.2010


 English version:
Journal of Mathematical Sciences (New York), 2011, 176:1, 1–6

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