By the method of fundamental inequalities, we study the equivalent convergence of two figured approximants for two-dimensional continued fractions, namely, the approximants obtained from the problem of correspondence of two-dimensional continued fractions to some formal double power series and the problem of equivalence of two-dimensional continued fractions. We also establish sufficient conditions under which the indicated two approximants of two-dimensional continued fractions converge to the same limit.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 4, pp. 7–14, October–December, 2015.
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Antonova, T.M., Sus’, O.M. Sufficient Conditions for the Equivalent Convergence of Sequences of Different Approximants for Two-Dimensional Continued Fractions. J Math Sci 228, 1–10 (2018). https://doi.org/10.1007/s10958-017-3601-3
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DOI: https://doi.org/10.1007/s10958-017-3601-3