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Zapiski Nauchnykh Seminarov POMI, 2001, Volume 276, Pages 41–51
(Mi znsl1411)
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This article is cited in 1 scientific paper (total in 1 paper)
On the regions of values of systems $\{f(z_0),f'(z_0),c_2\}$ and $\{f(r),f'(r),f(z_0)\}$ in the class of typically real functions
E. G. Goluzina St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
Let $T$ be the class of functions $f(z)$ having the following properties: these functions are regular and typically real in the disk $|z|<1$ and have the expansions $f(z)=z+c_2z^2+c_3z^3+\dotsb$. We give algebraic and geometric characterizations of regions of values for the functionals in the class $T$ mentioned in the title. In the same class of functions, we find regions of values for $f'(z_0)$ with fixed $c_2$ and $f(z_0)$ and for $f(z_0)$ with fixed $f(r)$ and $f'(r)$.
Received: 19.02.2001
Citation:
E. G. Goluzina, “On the regions of values of systems $\{f(z_0),f'(z_0),c_2\}$ and $\{f(r),f'(r),f(z_0)\}$ in the class of typically real functions”, Analytical theory of numbers and theory of functions. Part 17, Zap. Nauchn. Sem. POMI, 276, POMI, St. Petersburg, 2001, 41–51; J. Math. Sci. (N. Y.), 118:1 (2003), 4753–4759
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https://www.mathnet.ru/eng/znsl1411 https://www.mathnet.ru/eng/znsl/v276/p41
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