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A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions

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Abstract.

We give a Fekete-Szegö type inequality for an analytic function on the unit disk with Bloch seminorm ≤1. As an application of it, we derive a sharp inequality for the third coefficient of a uniformly locally univalent function f(z) = z + a 2 z 2 + a 3 z 3 + ⋯ on the unit disk with pre-Schwarzian norm ≤λ for a given λ > 0.

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Authors and Affiliations

  1. Hiroshima University, Higashi-Hiroshima, Japan

    Toshiyuki Sugawa & Takao Terada

Authors
  1. Toshiyuki Sugawa
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  2. Takao Terada
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Additional information

The first author was partially supported by the JSPS Grant-in-Aid for Scientific Research (B), 17340039.

Authors’ addresses: T. Sugawa and T. Terada, Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan

Current address: T. Sugawa, Division of Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai 980-8579, Japan

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Sugawa, T., Terada, T. A coefficient inequality for Bloch functions with applications to uniformly locally univalent functions. Monatsh Math 156, 167–173 (2009). https://doi.org/10.1007/s00605-008-0548-y

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  • DOI: https://doi.org/10.1007/s00605-008-0548-y

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