Journal
CARPATHIAN MATHEMATICAL PUBLICATIONS
Volume 13, Issue 3, Pages 619-630Publisher
VASYL STEFANYK PRECARPATHIAN NATL UNIV
DOI: 10.15330/cmp.13.3.619-630
Keywords
branched continued fraction; convergence; continued fraction; rational approximation
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Effective criteria of convergence for branched continued fractions of special form with positive elements were established using the criterion of convergence. The study of parabolic regions of convergence utilized the technique of element regions and value regions, with half-planes considered as value regions. A multidimensional analogue of Tron's twin convergence regions for branched continued fractions of the special form was established, providing conditions for the convergence of multidimensional S-fractions with independent variables.
Using the criterion of convergence of branched continued fractions of the special form with positive elements, effective sufficient criteria of convergence for these fractions are established. To study the parabolic regions of convergence, the element regions and value regions technique was used. In particular, half-planes are considered as value regions. A multidimensional analogue of Tron's twin convergence regions for branched continued fractions of the special form is established. The obtained results made it possible to establish the conditions for the convergence of the multidimensional S-fractions with independent variables.
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