Convergence criteria of branched continued fractions
The convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed. The classical theorems of convergence of continued fractions that have become the subject of multidimensional generalizations are formulated. The c...
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Oles Honchar Dnipro National University
2024-12-01
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| Series: | Researches in Mathematics |
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| Online Access: | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/432/432 |
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| author | I.B. Bilanyk D.I. Bodnar O.G. Vozniak |
| author_facet | I.B. Bilanyk D.I. Bodnar O.G. Vozniak |
| author_sort | I.B. Bilanyk |
| collection | DOAJ |
| description | The convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed. The classical theorems of convergence of continued fractions that have become the subject of multidimensional generalizations are formulated. The convergence conditions of branched continued fractions of the general form with positive elements are reviewed. The problem the solution of which caused changes in the structure of such branched continued fractions is formulated. A multidimensional generalization of the convergence criterion of branched continued fractions of the special form is stated. A multidimensional generalization of Worpitzky's and van Vleck's convergence theorems, the Śleszyński-Pringsheim theorem for the considered types of branched continued fractions are considered. The obtained multidimensional analogs of the theorems are analyzed, and other conditions of convergence, in particular, of branched continued fractions with real elements, multidimensional Leighton's and Wall's theorems, and others are given. |
| format | Article |
| id | doaj-art-b97fa5b01816437294d0c39f26b6e8e2 |
| institution | Kabale University |
| issn | 2664-4991 2664-5009 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Oles Honchar Dnipro National University |
| record_format | Article |
| series | Researches in Mathematics |
| spelling | doaj-art-b97fa5b01816437294d0c39f26b6e8e22025-01-05T19:30:10ZengOles Honchar Dnipro National UniversityResearches in Mathematics2664-49912664-50092024-12-01322536910.15421/242419Convergence criteria of branched continued fractionsI.B. Bilanyk0https://orcid.org/0000-0002-1120-6317D.I. Bodnar1O.G. Vozniak2Ternopil Volodymyr Hnatiuk National Pedagogical UniversityWest Ukrainian National UniversityWest Ukrainian National UniversityThe convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed. The classical theorems of convergence of continued fractions that have become the subject of multidimensional generalizations are formulated. The convergence conditions of branched continued fractions of the general form with positive elements are reviewed. The problem the solution of which caused changes in the structure of such branched continued fractions is formulated. A multidimensional generalization of the convergence criterion of branched continued fractions of the special form is stated. A multidimensional generalization of Worpitzky's and van Vleck's convergence theorems, the Śleszyński-Pringsheim theorem for the considered types of branched continued fractions are considered. The obtained multidimensional analogs of the theorems are analyzed, and other conditions of convergence, in particular, of branched continued fractions with real elements, multidimensional Leighton's and Wall's theorems, and others are given.https://vestnmath.dnu.dp.ua/index.php/rim/article/view/432/432continued fractionbranched continued fractionbranched continued fraction of the special formconvergence |
| spellingShingle | I.B. Bilanyk D.I. Bodnar O.G. Vozniak Convergence criteria of branched continued fractions Researches in Mathematics continued fraction branched continued fraction branched continued fraction of the special form convergence |
| title | Convergence criteria of branched continued fractions |
| title_full | Convergence criteria of branched continued fractions |
| title_fullStr | Convergence criteria of branched continued fractions |
| title_full_unstemmed | Convergence criteria of branched continued fractions |
| title_short | Convergence criteria of branched continued fractions |
| title_sort | convergence criteria of branched continued fractions |
| topic | continued fraction branched continued fraction branched continued fraction of the special form convergence |
| url | https://vestnmath.dnu.dp.ua/index.php/rim/article/view/432/432 |
| work_keys_str_mv | AT ibbilanyk convergencecriteriaofbranchedcontinuedfractions AT dibodnar convergencecriteriaofbranchedcontinuedfractions AT ogvozniak convergencecriteriaofbranchedcontinuedfractions |