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Locally convex functions and the Schwarzian derivative

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Abstract

In this paper we study various classes of locally convex analytic functions in the unit disc, which are invariant under the group of Möbius automorphisms of the unit disc. Bounds for the Schwarzian derivative of functions in these classes are achieved and used to obtain estimates for the uniform hyperbolic radius of univalence in these classes.

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Authors and Affiliations

  1. Department of Mathematics, Technion — Israel Institute of Technology, 32000, Haifa, Israel

    Reuven Harmelin

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  1. Reuven Harmelin
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Harmelin, R. Locally convex functions and the Schwarzian derivative. Israel J. Math. 67, 367–379 (1989). https://doi.org/10.1007/BF02764954

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  • DOI: https://doi.org/10.1007/BF02764954

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