^{1}Makarov, VL^{2}Pahirya, MM^{1}Institute of Mathematics of the NAS of Ukraine, Kyiv^{2}Mukachevo State University, Mukachevo |

Dopov. Nac. akad. nauk Ukr. 2018, 3:12-21 |

https://doi.org/10.15407/dopovidi2018.03.012 |

Section: Mathematics |

Language: Ukrainian |

Abstract: The problem of interpolation of a functional by an integral continued C-fraction if its value is known on the set of continual nodes is studied. The necessary and sufficient conditions for its solvability are found. In the partial case, such an integral continued fraction contains an interpolation continued C-fraction, which is used to approximate the functions of one variable. |

Keywords: continual nodes, integral continued C-fraction, interpolation of a functional |

References:

- Makarov, V. L. & Khlobistov, V. V. (1999). Fundamentals of the theory of polynomial operator interpolation. Kiev: Institute of Mathematics of the NAS of Ukraine (in Russian).
- Makarov, V. L., Khlobistov, V. V. & Yanovich, L. A. (2000). Interpolation of operators. Kiev: Naukova dumka (in Russian).
- Jones, W. & Tron, W. (1985). Continued fractions. Analytic theory and applications. Moscow: Mir (in Russian).
- Skorobogat'ko, V. Ya. (1983). Theory of Branching Continued Fractions and Its Application in Computational Mathematics. Moscow: Nauka (in Russian).
- Syavavko, M. S. (1994). Integral continued fractions. Kiev: Naukova dumka (in Ukrainian).
- Mykhal'chuk, B. R. (1999). Interpolation of nonlinear functionals by integral continued fractions. Ukr. Mat. Zhurn., 51, No. 3, pp. 364-375 (in Ukrainian). doi: https://doi.org/10.1007/BF02592477
- Makarov, V. L., Khlobistov, V. V. & Mykhal'chuk, B. R. (2003). Interpolation integral continued fractions. Ukr. Mat. Zhurn., 55, No. 4, pp. 479-488 (in Ukrainian). doi: https://doi.org/10.1023/B:UKMA.0000010158.50027.08
- Makarov, V. L. & Demkiv, I. I. (2008). A new class of interpolation integral continued fractions. Dopov. Nac. akad. nauk Ukr., No. 11, pp. 17-23 (in Ukrainian).
- Makarov, V. L., Khlobistov, V. V. & Demkiv, I. I. (2008). Interpolation integral operator fractions in a Banach space. Dopov. Nac. akad. nauk Ukr., No. 3, pp. 17-23 (in Ukrainian).
- 10. Makarov, V. L. & Demkiv, I. I. (2014). Interpolating integral continued fraction of Thiele type. Mat. Metody ta Fiz.-Mekh. Polya, 57, No. 4, pp. 44-50 (in Ukrainian).
- Makarov, V. L. & Demkiv, I. I. (2016). An integral interpolation chain fraction of Thiele type. Dopov. Nac. akad. nauk Ukr., No. 1, pp. 12-18 (in Ukrainian). doi: https://doi.org/10.15407/dopovidi2016.01.012
- Makarov, V. L. & Demkiv, I. I. (2016). Abstract interpolation Thiele-type fraction. Mat. Metody ta Fiz.-Mekh. Polya, 59, No. 2, pp. 50-57 (in Ukrainian).
- Pahirya, M. M. (2016). Approximation of functions by continued fractions. Uzhhorod: Grazda (in Ukrainian).
- Averbukh, V. I. & Smolyanov, O. G. (1967). The theory of differentiation in linear topological spaces. Uspehi Mat. Nauk, 22, No. 6, pp. 201-260 (in Russian). doi: https://doi.org/10.1070/RM1967v022n06ABEH003761
- Makarov, V. L., Khlobystov, V. V., Kashpur, E. F. & Mikhal'chuk B. R. (2003). Integral Newton-Type Polynomials with Continual Nodes. Ukr. Mat. Zhurn., 55, No. 6, pp. 779-789 (in Ukrainian). doi: https://doi.org/10.1023/B:UKMA.0000010594.60504.08