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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2011 Volume 395, Pages 20–30 (Mi znsl4640)

On the mutual change of values of a function and its coefficients in the class of typically real functions

E. G. Goluzina

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

Abstract: The paper coninues investigations of the well-known class $T$ of typically real functions $f(z)$ in the disk $U=\{z\colon|z|<1\}$. The region of values of the system $\{c_2,c_3,f(z_1),f(z_2)\}$ in the class $T$ is studied. The region of values of $f(z_2)$ in the class of functions $f\in T$ with fixed values $c_2,c_3$ and $f(z_1)$ is determined.

Key words and phrases: typically real function, region of values, coefficients of the problem.

UDC: 517.54

Received: 09.11.2011


 English version:
Journal of Mathematical Sciences (New York), 2012, 182:6, 754–760

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