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A self-duality of strong starlikeness. (English) Zbl 1079.30015
Given \(D^{v}\) the analytic inversion of the exterior of a \(D\)-simply connected domain, namely, \(D^{v}=\{w\in C:\frac{1}{w}\in\widehat{C}-\overline{D}\}\). The author shows that \(D\) is strongly starlike of order \(\alpha<1\) with respect to the origin if and only if so is \(D^{v}\). This explains the relationship between some known properties of strongly starlike domains and thus provides several new characterizations for the domains mentioned.

MSC:
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C20 Conformal mappings of special domains
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