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
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 41-51
Cet article a éte moissonné depuis la source Math-Net.Ru
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 $f'(r)$.
@article{ZNSL_2001_276_a2,
author = {E. G. Goluzina},
title = {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},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {41--51},
year = {2001},
volume = {276},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a2/}
}
TY - JOUR
AU - E. G. Goluzina
TI - 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
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2001
SP - 41
EP - 51
VL - 276
UR - http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a2/
LA - ru
ID - ZNSL_2001_276_a2
ER -
%0 Journal Article
%A E. G. Goluzina
%T 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
%J Zapiski Nauchnykh Seminarov POMI
%D 2001
%P 41-51
%V 276
%U http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a2/
%G ru
%F ZNSL_2001_276_a2
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. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 17, Tome 276 (2001), pp. 41-51. http://geodesic.mathdoc.fr/item/ZNSL_2001_276_a2/