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On Some Sequences of the Sets of Uniform Convergence for Two-Dimensional Continued Fractions

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For two-dimensional continued fractions whose elements belong to some rectangular sets of a complex plane, we establish the truncation error bound of their figured approximants. It is shown that the two-dimensional continued fractions are uniformly convergent with respect to a sequence of these rectangular sets.

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References

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Authors and Affiliations

  1. “L’vivs’ka Politekhnika” National University, Lviv, Ukraine

    T. M. Antonova

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

    O. M. Sus’

Authors
  1. T. M. Antonova
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  2. O. M. Sus’
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 1, pp. 47–56, January–March, 2015.

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Antonova, T.M., Sus’, O.M. On Some Sequences of the Sets of Uniform Convergence for Two-Dimensional Continued Fractions. J Math Sci 222, 56–69 (2017). https://doi.org/10.1007/s10958-017-3282-y

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  • DOI: https://doi.org/10.1007/s10958-017-3282-y

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