On one family of holomorphic in a circle of functions with positive real part of $n$th derivative
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 162-169
Voir la notice du chapitre de livre provenant de la source Math-Net.Ru
Let $\Phi(z)=z^n+b_2z^{n+1}+b_3z^{n+2}+\cdots$ be a holomorphic in the unit circle $|z|1$ function with $b_k\ge0$, $k=2,3,\dots$. Let $V_n(\Phi)$ be a family of functions $F(z)=z^n+a_2z^{n+1}+a_3z^{n+2}+\cdots$, for which $|a_k|\le b_k$, $k=2,3,\dots$. The radius of the greatest circle is established for which every function $F(z)\in V_n(\Phi)$ satisfies the condition $\operatorname{Re}F^{(n)}(z)>0$ .
Keywords:
holomorphic function, derivative, circle, family of functions, positive real part.
@article{UZKU_2009_151_3_a13,
author = {E. G. Kiriyatzkii},
title = {On one family of holomorphic in a~circle of functions with positive real part of $n$th derivative},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {162--169},
publisher = {mathdoc},
volume = {151},
number = {3},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a13/}
}
TY - JOUR AU - E. G. Kiriyatzkii TI - On one family of holomorphic in a circle of functions with positive real part of $n$th derivative JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2009 SP - 162 EP - 169 VL - 151 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a13/ LA - ru ID - UZKU_2009_151_3_a13 ER -
%0 Journal Article %A E. G. Kiriyatzkii %T On one family of holomorphic in a circle of functions with positive real part of $n$th derivative %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2009 %P 162-169 %V 151 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a13/ %G ru %F UZKU_2009_151_3_a13
E. G. Kiriyatzkii. On one family of holomorphic in a circle of functions with positive real part of $n$th derivative. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 162-169. http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a13/