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Avkhadiev–Becker Type Univalence Conditions for Biharmonic Mappings

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Abstract

In this paper we consider complex-valued biharmonic functions that are locally univalent. We construct families of biharmonic univalent mappings of the unite disc similar to Avkhadiev- Becker type conditions for analytic functions. Also, we investigate the case where biharmonic functions are defined on the exterior of the unit disc. In this case we obtain three analogs of Avkhadiev–Becker type conditions of univalence.

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Authors and Affiliations

  1. N. I. Lobachevskii Institute ofMathematics and Mechanics, Kazan Federal University, ul. Kremlevskaya 35, Kazan, Tatarstan, 420008, Russia

    R. G. Nasibullin

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  1. R. G. Nasibullin
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Correspondence to R. G. Nasibullin.

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Submitted by F. G. Avkhadiev

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Nasibullin, R.G. Avkhadiev–Becker Type Univalence Conditions for Biharmonic Mappings. Lobachevskii J Math 39, 794–802 (2018). https://doi.org/10.1134/S1995080218060124

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  • DOI: https://doi.org/10.1134/S1995080218060124

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