Geodesic
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
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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. 
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     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},
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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/

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