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Fatou’s Theorem for A(z)-Analytic Functions

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Abstract

We consider \(A(z)\)-analytic functions in case when \(A(z)\) is anti-analytic function. This paper investigates the behavior near the boundary of the derivative of the function, \(A(z)\)-analytic inside the \(A(z)\)-lemniscate and with a bounded change of it at the boundary. Thus, this paper introduces the complex Lipschitz condition for \(A(z)\)-analytic functions and proves Fatou’s theorem for \(A(z)\)-analytic functions.

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Authors and Affiliations

  1. Belorussian-Uzbek Joint Intersectoral Institute of Applied Technical Qualifications in Tashkent, Kibraisky district, 100071, Tashkent, Uzbekistan

    N. M. Zhabborov

  2. Bukhara State University, 705018, Bukhara, Uzbekistan

    B. E. Husenov

Authors
  1. N. M. Zhabborov
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  2. B. E. Husenov
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Correspondence to N. M. Zhabborov or B. E. Husenov.

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Zhabborov, N.M., Husenov, B.E. Fatou’s Theorem for A(z)-Analytic Functions. Russ Math. 67, 9–16 (2023). https://doi.org/10.3103/S1066369X23070101

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  • DOI: https://doi.org/10.3103/S1066369X23070101

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