Abstract
The infinite branched continued fraction, associated with the correspondence problem between a formal double power series and a sequence of the rational approximations of a function of two variables, is considered. Using formulas for real and imaginary parts of tails of figured approximants and a multidimensional analogue of the Stieltjes–Vitali theorem, the figured uniform convergence of such a fraction in some domain is investigated and the estimation of the rate of its convergence is obtained. Cite as: T. M. Antonova, S. M. Vozna, “On convergence of one class of corresponding two-dimensional branched continued fractions,” Prykl. Probl. Mekh. Mat. , Issue 18, 25–33 (2020) (in Ukrainian), https://doi.org/10.15407/apmm2020.18.25-33
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