Abstract
Univalent functions with quasiconformal extension are important in the theory of Teichmüller spaces as well as being interesting for their own sake. In this paper we obtain the exact bound for the coefficients of functions in the class S(k) of normalized univalent functions on the unit disk with k-quasiconformal extension, where k is small. This answers a question of Kühnau and Niske [13]. The method is based on application of the known properties of extremal quasiconformal mappings and on the generalization of the Schwarz lemma.
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© 1988 Springer-Verlag New York Inc.
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Krushkal’, S.L. (1988). The coefficient problem for univalent functions with quasiconformal extension. In: Drasin, D., Kra, I., Earle, C.J., Marden, A., Gehring, F.W. (eds) Holomorphic Functions and Moduli I. Mathematical Sciences Research Institute Publications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9602-4_13
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DOI: https://doi.org/10.1007/978-1-4613-9602-4_13
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