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Exact Regions of Mutual Variation of Coefficients of Holomorphic Self-Maps of a Disc with Fixed Points

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Abstract

A method is proposed that allows obtaining the exact regions of mutual variation of Taylor coefficients of holomorphic self-maps of a disc with an interior fixed point and an arbitrary finite set of different boundary fixed points. Based on this method, exact inequalities for the first and second coefficients are obtained.

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Funding

The study was supported by the Russian Science Foundation, project no. 22-11-00129, at Moscow State University.

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Authors and Affiliations

  1. Moscow Center of Fundamental and Applied Mathematics, Moscow State University, 119991, Moscow, Russia

    O. S. Kudryavtseva

  2. Volgograd State Technical University, 400005, Volgograd, Russia

    O. S. Kudryavtseva

Authors
  1. O. S. Kudryavtseva
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Correspondence to O. S. Kudryavtseva.

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The author declares that she has no conflicts of interest.

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Translated by E. Oborin

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Kudryavtseva, O.S. Exact Regions of Mutual Variation of Coefficients of Holomorphic Self-Maps of a Disc with Fixed Points. Russ Math. 67, 41–49 (2023). https://doi.org/10.3103/S1066369X23050079

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  • DOI: https://doi.org/10.3103/S1066369X23050079

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