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Convergence and Estimation of the Truncation Error for the Corresponding Two-Dimensional Continued Fractions

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Ukrainian Mathematical Journal Aims and scope

For the corresponding two-dimensional continued fractions with complex partial numerators that belong to certain subsets of the Cartesian product of two angular sets in the right half plane and partial denominators equal to one, we establish sufficient conditions for the uniform convergence and an estimate for the truncation error by using an analog of the method of fundamental inequalities, relations for the real and imaginary parts of the tails of figured approximants, and a multidimensional analog of the Stieltjes–Vitali theorem.

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Author information

Authors and Affiliations

  1. Lviv Polytechnic National University, Lviv, Ukraine

    T. M. Antonova

  2. Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    O. M. Sus’

  3. Lviv Polytechnic National University, Lviv, Ukraine

    S. M. Vozna

Authors
  1. T. M. Antonova
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  2. O. M. Sus’
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  3. S. M. Vozna
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Correspondence to T. M. Antonova.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 4, pp. 443–457, April, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i4.7031.

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Antonova, T.M., Sus’, O.M. & Vozna, S.M. Convergence and Estimation of the Truncation Error for the Corresponding Two-Dimensional Continued Fractions. Ukr Math J 74, 501–518 (2022). https://doi.org/10.1007/s11253-022-02079-1

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  • DOI: https://doi.org/10.1007/s11253-022-02079-1

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