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Avkhadiev–Lehto Type Constants in the Study of the Gakhov Class

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Abstract

Avkhadiev's classes consist of holomorphic functions with a two-sided restriction on the module of the derivative. We study these classes in domains different from the unit disk. For the images of the domains under the mappings of Avkhadiev's classes, we find conditions providing the uniqueness of critical point of the conformal radius. We use an analogue of the concept that Lehto applied to study univalence of functions satisfying the conditions of Nehari type in domains conformally equivalent to a disk.

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ACKNOWLEDGMENTS

The authors express their sincere gratitude to the anonymous referee for remarks which essentially improve the text of the paper.

Funding

The work is fulfilled under the financial support of the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan, project no. 18-41-160017.

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Authors and Affiliations

  1. Kazan Federal University, 18 Kremlyovskaya str., 420008, Kazan, Russia

    A. V. Kazantsev & M. I. Kinder

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  1. A. V. Kazantsev
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  2. M. I. Kinder
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Correspondence to A. V. Kazantsev or M. I. Kinder.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 3, pp. 47–55.

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Kazantsev, A.V., Kinder, M.I. Avkhadiev–Lehto Type Constants in the Study of the Gakhov Class. Russ Math. 65, 43–50 (2021). https://doi.org/10.3103/S1066369X2103004X

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  • DOI: https://doi.org/10.3103/S1066369X2103004X

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