Abstract
The Roper-Suffridge extension operator provides a way of extending a (locally) univalent functionfεH(U) to a (locally) biholomorphic mappingF∈H(Bn). In this paper, we give a simplified proof of the Roper-Suffridge theorem: iff is convex, then so isF. We also show that iff∈S *, theF is starlike and that iff is a Bloch function inU, thenF is a Bloch mapping onB n. Finally, we investigate some open problems.
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Partially supported by the Natural Sciences and Engineering Research Council of Canada under grant A9221.
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Graham, I., Kohr, G. Univalent mappings associated with the Roper-Suffridge extension operator. J. Anal. Math. 81, 331–342 (2000). https://doi.org/10.1007/BF02788995
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DOI: https://doi.org/10.1007/BF02788995