Higher derivatives of holomorphic function with positive real part (Q1977494)

The author derives upper estimates for \(|f^{(n)}(z) |/ \text{Re} (f(z))\), \(n\geq 2,z\) in the unit disk \(D\), resp. in a hyperbolic domain \(\Omega\), where \(f\) is holomorphic in \(D\), respectively in \(\Omega\) and has positive real part there. The result for the unit disk part has been shown already by \textit{St. Ruscheweyh} in Bericht Nr. 7. Graz: Mathematisch-statistische Sektion im Forschungszentrum Graz (1974; Zbl 0274.30006).