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The growth theorem for strongly starlike mappings of order \(\alpha\) on bounded starlike circular domains. (English) Zbl 0983.32002
A Koebe’s type distortion theorem is proved for a certain class of starlike mappings on bounded circular starlike domains in \(\mathbb{C}^n\).
There are numerous misprints in the paper. In particular, in Theorem 2, relation (2) should be read as \[ \rho(z) \exp\int_0^{\rho(z)} \left[ \left( {1-t\over 1+t} \right)^\alpha- 1\right]{dt\over t}\leq\rho \bigl(f(z) \bigr) \leq\rho(z) \exp\int_0^{\rho(z)} \left[\left({1+t \over 1-t}\right)^\alpha -1\right] {dt\over t}, \] and the value \(r(\alpha)\) as \[ r(\alpha) =\exp \int^1_0 \left[\left({1-t \over 1+t}\right)^\alpha-1 \right]{dt\over t}. \]

MSC:
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
32A17 Special families of functions of several complex variables
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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