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On Landau’s Type Estimates for Coefficients of Univalent Functions

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Abstract

In this article we estimate the sum of coefficients for functions with restrictions on the pre-Schwarzian derivative. We obtain an estimate, which is sharp up to a constant and find upper and lower bounds for that constant. Also we estimate the sum of the first three coefficients for all functions f, such that \(\log f'(z)\) is bounded with respect to the Bloch norm.

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Acknowledgements

The research of I.R. Kayumov and D.M. Khammatova was funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities, project 1.13556.2019/13.1.

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Authors and Affiliations

  1. Kazan Federal University, Kazan, Russia

    I. R. Kayumov & D. M. Khammatova

  2. Technical University of Braunschweig, Brunswick, Germany

    K.-J. Wirths

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  1. I. R. Kayumov
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  2. D. M. Khammatova
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  3. K.-J. Wirths
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Correspondence to I. R. Kayumov.

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Communicated by Vladimir V. Andrievskii.

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Kayumov, I.R., Khammatova, D.M. & Wirths, KJ. On Landau’s Type Estimates for Coefficients of Univalent Functions. Comput. Methods Funct. Theory 20, 511–521 (2020). https://doi.org/10.1007/s40315-020-00333-w

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  • DOI: https://doi.org/10.1007/s40315-020-00333-w

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