Bodnar, D. I.; Bodnar, O. S.; Bilanyk, I. B. A truncation error bound for branched continued fractions of the special form on subsets of angular domains. (English) Zbl 07797249 Carpathian Math. Publ. 15, No. 2, 437-448 (2023). MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} et al., Carpathian Math. Publ. 15, No. 2, 437--448 (2023; Zbl 07797249) Full Text: DOI
Bilanyk, I. B.; Bodnar, D. I. Two-dimensional generalization of the Thron-Jones theorem on the parabolic domains of convergence of continued fractions. (English. Ukrainian original) Zbl 1515.30017 Ukr. Math. J. 74, No. 9, 1317-1333 (2023); translation from Ukr. Mat. Zh. 74, No. 9, 1155-1169 (2022). MSC: 30B70 PDFBibTeX XMLCite \textit{I. B. Bilanyk} and \textit{D. I. Bodnar}, Ukr. Math. J. 74, No. 9, 1317--1333 (2023; Zbl 1515.30017); translation from Ukr. Mat. Zh. 74, No. 9, 1155--1169 (2022) Full Text: DOI
Bodnar, D. I.; Bilanyk, I. B. Parabolic convergence regions of branched continued fractions of the special form. (English) Zbl 1486.30010 Carpathian Math. Publ. 13, No. 3, 619-630 (2021). MSC: 30B70 40A15 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{I. B. Bilanyk}, Carpathian Math. Publ. 13, No. 3, 619--630 (2021; Zbl 1486.30010) Full Text: DOI
Bodnar, D. I.; Bilanyk, I. B. Estimates of the pointwise and uniform convergence rate of branched continued fractions with nonequivalent variables. (Ukrainian, English) Zbl 1463.40015 Mat. Metody Fiz.-Mekh. Polya 62, No. 4, 72-82 (2019). Reviewer: L. N. Chernetskaja (Kyïv) MSC: 40A15 30B70 11A55 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{I. B. Bilanyk}, Mat. Metody Fiz.-Mekh. Polya 62, No. 4, 72--82 (2019; Zbl 1463.40015)
Bodnar, D. I.; Dmytryshyn, R. I. Multidimensional associated fractions with independent variables and multiple power series. (English. Ukrainian original) Zbl 1435.32006 Ukr. Math. J. 71, No. 3, 370-386 (2019); translation from Ukr. Mat. Zh. 71, No. 3, 325-349 (2019). MSC: 32A30 30B70 40A15 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{R. I. Dmytryshyn}, Ukr. Math. J. 71, No. 3, 370--386 (2019; Zbl 1435.32006); translation from Ukr. Mat. Zh. 71, No. 3, 325--349 (2019) Full Text: DOI
Bilanyk, I.; Bodnar, D. I.; Buyak, L. Representation of a quotient of solutions of a four-term linear recurrence relation in the form of a branched continued fraction. (English) Zbl 1420.11015 Carpathian Math. Publ. 11, No. 1, 33-41 (2019). MSC: 11A55 11J70 30B70 40A15 PDFBibTeX XMLCite \textit{I. Bilanyk} et al., Carpathian Math. Publ. 11, No. 1, 33--41 (2019; Zbl 1420.11015) Full Text: DOI
Bodnar, D. I.; Bilanyk, I. B. Convergence criterion for branched contnued fractions of the special form with positive elements. (English) Zbl 1370.40003 Carpathian Math. Publ. 9, No. 1, 13-21 (2017). MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{I. B. Bilanyk}, Carpathian Math. Publ. 9, No. 1, 13--21 (2017; Zbl 1370.40003) Full Text: DOI
Bodnar, D. I.; Voznyak, O. G.; Myhalchuk, R. I. Convergence criteria for branched continued fraction with positive elements. (Ukrainian, English) Zbl 1349.40007 Mat. Metody Fiz.-Mekh. Polya 58, No. 1, 57-64 (2015); translation in J. Math. Sci., New York 222, No. 1, 70-80 (2017). Reviewer: R. V. Mullajonov (Andizhan) MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} et al., Mat. Metody Fiz.-Mekh. Polya 58, No. 1, 57--64 (2015; Zbl 1349.40007); translation in J. Math. Sci., New York 222, No. 1, 70--80 (2017) Full Text: DOI
Bodnar, D. I.; Bubniak, M. M. On convergence \((2,1,\ldots,1)\)-periodic branched continued fraction of the special form. (On convergence of \((2,1,\ldots,1)\)-periodic branched continued fraction of the special form.) (English) Zbl 1329.40002 Carpathian Math. Publ. 7, No. 2, 148-154 (2015). MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{M. M. Bubniak}, Carpathian Math. Publ. 7, No. 2, 148--154 (2015; Zbl 1329.40002) Full Text: DOI
Bodnar, D. I.; Bubnyak, M. M. Multidimensional generalization of the oval theorem for periodic branched continued fraction of a special form. (Ukrainian. English summary) Zbl 1340.40003 Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 54-67 (2014). MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{M. M. Bubnyak}, Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 4, 54--67 (2014; Zbl 1340.40003)
Bodnar, D. I.; Bubniak, M. M. Rate estimates of pointwise and uniform convergence of 1-periodic branching continued fraction of special form. (Ukrainian, English) Zbl 1313.30012 Mat. Metody Fiz.-Mekh. Polya 56, No. 4, 24-32 (2013); translation in J. Math. Sci., New York 208, No. 3, 289-300 (2015). Reviewer: L. N. Chernetskaja (Kyïv) MSC: 30B70 40A15 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{M. M. Bubniak}, Mat. Metody Fiz.-Mekh. Polya 56, No. 4, 24--32 (2013; Zbl 1313.30012); translation in J. Math. Sci., New York 208, No. 3, 289--300 (2015) Full Text: DOI
Bodnar, D. I.; Zatorsky, R. A. Generalization of continued fractions. II. (Ukrainian, English) Zbl 1274.40010 Mat. Metody Fiz.-Mekh. Polya 54, No. 2, 43-50 (2011); translation in J. Math. Sci., New York 184, No. 1, 46-55 (2012). Reviewer: L. N. Chernetskaja (Kyïv) MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{R. A. Zatorsky}, Mat. Metody Fiz.-Mekh. Polya 54, No. 2, 43--50 (2011; Zbl 1274.40010); translation in J. Math. Sci., New York 184, No. 1, 46--55 (2012)
Bodnar, D. I.; Dmytryshyn, R. I. A two-dimensional generalization of the Bauer algorithm. (Ukrainian. English summary) Zbl 1088.40001 Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2006, No. 2, 13-18 (2006). MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{R. I. Dmytryshyn}, Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 2006, No. 2, 13--18 (2006; Zbl 1088.40001)
Bodnar, D. I. Multidimensional generalizations of continued fractions. (Ukrainian) Zbl 1076.40502 Mat. Metody Fiz.-Mekh. Polya 46, No. 3, 32-39 (2003). Reviewer: L. N. Chernetskaja (Kyïv) MSC: 40A15 30B70 40-02 30-02 PDFBibTeX XMLCite \textit{D. I. Bodnar}, Mat. Metody Fiz.-Mekh. Polya 46, No. 3, 32--39 (2003; Zbl 1076.40502)
Bodnar, D. I.; Gladun, V. R. Sufficient conditions of stability of branching continued fractions with positive elements. (Ukrainian) Zbl 1073.30004 Mat. Metody Fiz.-Mekh. Polya 45, No. 1, 22-27 (2002). Reviewer: V. G. Miladzhanov (Andizhan) MSC: 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{V. R. Gladun}, Mat. Metody Fiz.-Mekh. Polya 45, No. 1, 22--27 (2002; Zbl 1073.30004)
Bodnar, D. I.; Dmytryshyn, R. I. On the convergence of multidimensional \(g\)-fraction. (English) Zbl 0984.40006 Mat. Stud. 15, No. 2, 115-126 (2001). MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{R. I. Dmytryshyn}, Mat. Stud. 15, No. 2, 115--126 (2001; Zbl 0984.40006)
Antonova, T. M.; Bodnar, D. I. Domains of convergence of branching continued fractions of a special type. (Ukrainian. English summary) Zbl 1022.40004 Kovtunets, V. V. (ed.), Approximation theory and its applications. Proceedings of the international conference dedicated to the memory of Vladislav Kirillovich Dzyadyk held in Kiev, Ukraine, May 27-31, 1999. Kyïv: Instytut Matematyky NAN Ukraïny. Pr. Inst. Mat. Nats. Akad. Nauk Ukr., Mat. Zastos. 31, 19-32 (2000). Reviewer: A.M.Gomilko (Kyïv) MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{T. M. Antonova} and \textit{D. I. Bodnar}, in: Teoriya nablyzhennya funktsij ta ïï zastosuvannya. Kyïv: Instytut Matematyky NAN Ukraïny. 19--32 (2000; Zbl 1022.40004)
Bodnar, D. I.; Kuchmins’ka, Kh. Yo. An analog of the Van Vleck theorem for two-dimensional continued fractions. (Ukrainian) Zbl 1046.40003 Mat. Metody Fiz.-Mekh. Polya 42, No. 4, 21-25 (1999). Reviewer: L. N. Chernetskaja (Kyïv) MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{Kh. Yo. Kuchmins'ka}, Mat. Metody Fiz.-Mekh. Polya 42, No. 4, 21--25 (1999; Zbl 1046.40003)
Bodnar, D. I. On the convergence of branched continued fractions. (English. Ukrainian original) Zbl 0980.40001 J. Math. Sci., New York 97, No. 1, 3862-3871 (1999); translation from Mat. Metody Fiz.-Mekh. Polya 41, No. 1, 117-126 (1998). Reviewer: L. N. Chernetskaja (Kyïv) MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar}, Mat. Metody Fiz.-Mekh. Polya 41, No. 1, 117--126 (1998; Zbl 0980.40001); translation from Mat. Metody Fiz.-Mekh. Polya 41, No. 1, 117--126 (1998)
Bodnar, D. I.; Kuchmins’ka, Kh. J. Branching continued fractions (on the 30th anniversary of the first publication). (Ukrainian) Zbl 0891.01029 Mat. Metody Fiz.-Mekh. Polya 39, No. 2, 9-19 (1996). Reviewer: L.N.Chernetskaya (Kyïv) MSC: 01A60 40-03 11A55 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{Kh. J. Kuchmins'ka}, Mat. Metody Fiz.-Mekh. Polya 39, No. 2, 9--19 (1996; Zbl 0891.01029)
Bodnar, D. I.; Kuchmins’ka, Kh. J. Branched continued fractions (30th anniversary of the first publication). (English. Ukrainian original) Zbl 0899.01015 J. Math. Sci., New York 90, No. 5, 2324-2333 (1998); translation from Mat. Metody Fiz.-Mekh. Polya 39, No. 2, 9-19 (1996). MSC: 01A60 40-03 11A55 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{Kh. J. Kuchmins'ka}, Mat. Metody Fiz.-Mekh. Polya 39, No. 2, 9--19 (1996; Zbl 0899.01015); translation from Mat. Metody Fiz.-Mekh. Polya 39, No. 2, 9--19 (1996)
Bodnar, D. I.; Kuchmins’ka, Kh. Yo. Parabolic convergence region for two-dimensional continued functions. (Ukrainian) Zbl 1053.30504 Mat. Stud. 4, 29-36 (1995). MSC: 30B70 40A15 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{Kh. Yo. Kuchmins'ka}, Mat. Stud. 4, 29--36 (1995; Zbl 1053.30504)
Bodnar, D. I. On Koch’s convergence criterion for branching continued fractions. (English) Zbl 1267.30009 J. Sov. Math. 67, No. 5, 3265-3268 (1993); translation from Mat. Metody Fiz.-Mekh. Polya, No. 36, 10–13 (1992). MSC: 30B70 40A15 PDFBibTeX XMLCite \textit{D. I. Bodnar}, J. Sov. Math. 67, No. 5, 3265--3268 (1993; Zbl 1267.30009); translation from Mat. Metody Fiz.-Mekh. Polya, No. 36, 10--13 (1992) Full Text: DOI
Bodnar, D. I. Expansion of a ratio of hypergeometric functions of two variables in branching continued fractions. (English) Zbl 1267.33005 J. Sov. Math. 64, No. 5, 1155-1158 (1993); translation from Mat. Metody Fiz.-Mekh. Polya, No. 32, 40–44 (1990). MSC: 33C20 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar}, J. Sov. Math. 64, No. 5, 1155--1158 (1993; Zbl 1267.33005); translation from Mat. Metody Fiz.-Mekh. Polya, No. 32, 40--44 (1990) Full Text: DOI
Bodnar, D. I. Two-dimensional corresponding branching continued fractions with partial numerators which are linear with respect to variables. (Russian. English summary) Zbl 0715.40002 Dokl. Akad. Nauk Ukr. SSR, Ser. A 1990, No. 10, 3-6 (1990). MSC: 40A15 40B05 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar}, Dokl. Akad. Nauk Ukr. SSR, Ser. A 1990, No. 10, 3--6 (1990; Zbl 0715.40002)
Bodnar, D. I. Pringsheim-type convergence indicators for branching continued fractions. (English. Russian original) Zbl 0729.40001 Ukr. Math. J. 41, No. 11, 1339-1343 (1989); translation from Ukr. Mat. Zh. 41, No. 11, 1553-1557 (1989). Reviewer: P.Wynn (Mexico) MSC: 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar}, Ukr. Math. J. 41, No. 11, 1339--1343 (1989; Zbl 0729.40001); translation from Ukr. Mat. Zh. 41, No. 11, 1553--1557 (1989) Full Text: DOI
Bodnar, D. I. Convergence tests for multidimensional analogs of \(g\)-fractions. (Russian) Zbl 0711.30007 Methods for the investigations of differential and integral operators, Collect. Sci. Works, Kiev, 22-27 (1989). Reviewer: G. Lopez Lagomasino MSC: 30B70 40A15 PDFBibTeX XML
Bodnar, D. I. Analogons of the Pringsheim convergence test for branching continued fractions. (Russian. English summary) Zbl 0706.40002 Dokl. Akad. Nauk Ukr. SSR, Ser. A 1988, No. 10, 36-39 (1988). Reviewer: P.Wynn MSC: 40A15 41A25 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar}, Dokl. Akad. Nauk Ukr. SSR, Ser. A 1988, No. 10, 36--39 (1988; Zbl 0706.40002)
Bodnar, D. I. Branched continued fractions. (Ветвящиеся цепные дроби.) (Russian) Zbl 1416.40001 Kiev: Naukova Dumka. 176 p. (1986). MSC: 40-02 40A15 30B70 11A55 PDFBibTeX XMLCite \textit{D. I. Bodnar}, Ветвящиеся цепные дроби (Russian). Kiev: Naukova Dumka (1986; Zbl 1416.40001) Full Text: Link
Bodnar, D. I.; Kuchminskaya, Kh. I. On the convergence of expansion of functions of two variables in corresponding branching continued fractions. (Russian) Zbl 0439.40001 Mat. Metody Fiz.-Mekh. Polya 11, 3-6 (1980). MSC: 40A15 41A60 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar} and \textit{Kh. I. Kuchminskaya}, Mat. Metody Fiz.-Mekh. Polya 11, 3--6 (1980; Zbl 0439.40001)
Bodnar, D. I. An analogue of Worpitzky’s convergence test for branching continued fractions. (Ukrainian) Zbl 0453.40002 Questions of qualitative theory of differential equations and their applications, Collect. sci. Works, Acad. Sci. Ukr. SSR, Inst. Math., Kiev, 7-8 (1978). Reviewer: Tibor Šalát (Bratislava) MSC: 40A15 30B70 PDFBibTeX XML
Bodnar, D. I. On a generalisation of Seidel’s convergence criterion for branching continued fractions. (Russian) Zbl 0435.40005 Math. Collect., Acad. Sci. Ukr. SSR, Inst. Math. 155, 44-47 (1976). MSC: 40A15 30B70 PDFBibTeX XML
Bodnar, D. I. An analogue of Worpitzky’s convergence criterion for branching continued fractions. (Russian) Zbl 0435.40004 Math. Collect., Acad. Sci. Ukr. SSR, Inst. Math. 155, 40-43 (1976). MSC: 40A15 30B70 32A05 PDFBibTeX XML
Bodnar, D. I. Error estimation in calculation of branching continued fractions. (Ukrainian) Zbl 0327.65017 Dopov. Akad. Nauk Ukr. RSR, Ser. A 1975, 1059-1062 (1975). MSC: 65D15 40A15 30B70 PDFBibTeX XMLCite \textit{D. I. Bodnar}, Dopov. Akad. Nauk Ukr. RSR, Ser. A 1975, 1059--1062 (1975; Zbl 0327.65017)