On the convergence of multidimensional S-fractions with independent variables
In this paper, we investigate the convergence of multidimensional S-fractions with independent variables, which are a multidimensional generalization of S-fractions. These branched continued fractions are an efficient tool for the approximation of multivariable functions, which are represented by fo...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2018-07-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/1469 |
| _version_ | 1828888072242069504 |
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| author | O.S. Bodnar R.I. Dmytryshyn |
| author_facet | O.S. Bodnar R.I. Dmytryshyn |
| author_sort | O.S. Bodnar |
| collection | DOAJ |
| description | In this paper, we investigate the convergence of multidimensional S-fractions with independent variables, which are a multidimensional generalization of S-fractions. These branched continued fractions are an efficient tool for the approximation of multivariable functions, which are represented by formal multiple power series. For establishing the convergence criteria, we use the convergence continuation theorem to extend the convergence, already known for a small region, to a larger region. As a result, we have shown that the intersection of the interior of the parabola and the open disk is the domain of convergence of a multidimensional S-fraction with independent variables. And, also, we have shown that the interior of the parabola is the domain of convergence of a branched continued fraction, which is reciprocal to the multidimensional S-fraction with independent variables. In addition, we have obtained two new convergence criteria for S-fractions as a consequences from the above mentioned results. |
| first_indexed | 2024-12-13T12:16:07Z |
| format | Article |
| id | doaj.art-97242f5d9c754166a1a6626647000526 |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-13T12:16:07Z |
| publishDate | 2018-07-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-97242f5d9c754166a1a66266470005262022-12-21T23:46:43ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102018-07-01101586410.15330/cmp.10.1.58-641469On the convergence of multidimensional S-fractions with independent variablesO.S. Bodnar0R.I. Dmytryshyn1Volodymyr Gnatiuk Ternopil National Pedagogical University, 2 Kryvonosa str., 46027, Ternopil, UkraineVasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineIn this paper, we investigate the convergence of multidimensional S-fractions with independent variables, which are a multidimensional generalization of S-fractions. These branched continued fractions are an efficient tool for the approximation of multivariable functions, which are represented by formal multiple power series. For establishing the convergence criteria, we use the convergence continuation theorem to extend the convergence, already known for a small region, to a larger region. As a result, we have shown that the intersection of the interior of the parabola and the open disk is the domain of convergence of a multidimensional S-fraction with independent variables. And, also, we have shown that the interior of the parabola is the domain of convergence of a branched continued fraction, which is reciprocal to the multidimensional S-fraction with independent variables. In addition, we have obtained two new convergence criteria for S-fractions as a consequences from the above mentioned results.https://journals.pnu.edu.ua/index.php/cmp/article/view/1469convergenceuniform convergencemultidimensional s-fraction with independent variables |
| spellingShingle | O.S. Bodnar R.I. Dmytryshyn On the convergence of multidimensional S-fractions with independent variables Karpatsʹkì Matematičnì Publìkacìï convergence uniform convergence multidimensional s-fraction with independent variables |
| title | On the convergence of multidimensional S-fractions with independent variables |
| title_full | On the convergence of multidimensional S-fractions with independent variables |
| title_fullStr | On the convergence of multidimensional S-fractions with independent variables |
| title_full_unstemmed | On the convergence of multidimensional S-fractions with independent variables |
| title_short | On the convergence of multidimensional S-fractions with independent variables |
| title_sort | on the convergence of multidimensional s fractions with independent variables |
| topic | convergence uniform convergence multidimensional s-fraction with independent variables |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/1469 |
| work_keys_str_mv | AT osbodnar ontheconvergenceofmultidimensionalsfractionswithindependentvariables AT ridmytryshyn ontheconvergenceofmultidimensionalsfractionswithindependentvariables |