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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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