Romanyuk Anatolii
Publications
$\hspace{75mm} \normalsize{2024}$
• Pozharska K., Romanyuk A. The best m-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$. Researches in Mathematics, 2024, 32 (2), 137-154.
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/438
• Pozharska K., Romanyuk A., Romanyuk V. Widths and entropy numbers of the classes of periodic functions of one and several variables in the space $B_{q,1}$. Carpathian Math. Publ. 2024, 16 (2), 351–366.
https://doi.org/10.15330/cmp.16.2.351-366
• Pozharska K., Romanyuk A., Yanchenko S. Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative. Ukr. Math. J. 2024, 76 (7), 1144–1162; Translated from Ukrains’kyi Matematychnyi Zhurnal 2024, Vol. 76 (7), 1007-1023.
https://doi.org/10.1007/s11253-024-02378-9
$\hspace{75mm} \normalsize{2023}$
• Romanyuk A.S., Romanyuk V.S., Pozharska K.V., Hembars’ka S.B.Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions. Carpathian Math. Publ. 2023, 15 (1), 78–94.
https://doi.org/10.15330/cmp.15.1.78-94
• Romanyuk A.S., Yanchenko S.Ya. Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi-continuous functions. Math. Nachr. 2023, Vol. 296 (6), 2575–2587.
https://onlinelibrary.wiley.com/doi/10.1002/mana.202100202
$\hspace{75mm} \normalsize{2022}$
• Romanyuk A.S., Yanchenko S.Ya. Approximation of the classes of periodic functions of one and many variables from the Nikol’skii-Besov and Sobolev spaces. Ukrainian Math. J. 2022, Vol. 74 (6), 967-980; Translated from Ukrains’kyi Matematychnyi Zhurnal 2022, Vol. 74 (6), 844-855.
https://link.springer.com/article/10.1007/s11253-022-02110-5
• Romanyuk A.S., Yanchenko S.Ya. Kolmogorov widths of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasicontinuous functions. Ukr. Math. J. 2022, V. 74, Issue 2, pp. 251–265; Translated from Ukrains’kyi Matematychnyi Zhurnal, V. 74, No. 2, pp. 220–232, February 2022.
https://link.springer.com/article/10.1007/s11253-022-02061-x
• Romanyuk A.S., Yanchenko S.Ya. Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space $B_{1,1}$. Ukr. Math. J. February 2022, V. 73, Issue 8, pp. 1278–1298; Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 8, pp. 1102–1119, August, 2021.
https://link.springer.com/article/10.1007/s11253-022-01990-x
$\hspace{75mm} \normalsize{2021}$
• Romanyuk A.S., Romanyuk V.S. Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol’skii–Besov spaces. J. Math. Sci. 2021, 252 (4), 508–525.
https://doi.org/10.1007/s10958-020-05177-2
$\hspace{75mm} \normalsize{2020}$
• Romanyuk A.S., Romanyuk V.S. Estimation of Some Approximating Characteristics of the Classes of Periodic Functions of One and Many Variables. Ukrainian Math. J. 2020, 71 (8), 1257-1272.
https://doi.org/10.1007/s11253-019-01711-x
$\hspace{75mm} \normalsize{2019}$
• Romanyuk A.S. Entropy numbers and widths for the Nikol’skii - Besov classes of functions of many variables in the space $L_{\infty}$. Anal. Math. 2019, 45 (1), 133–151. https://doi.org/10.1007/s10476-018-0611-4
• Romanyuk A.S., Romanyuk V.S. Approximating Characteristics of the Classes of Periodic Multivariate Functions in the Space $B_{\infty,1}$. Ukrainian Math. J., 2019, V. 71, Issue 2, 308-321. https://doi.org/10.1007/s11253-019-01646-3
$\hspace{75mm} \normalsize{2018}$
• Romanyuk A.S. Kolmogorov Widths and Bilinear Approximations of the Classes of Periodic Functions of One and Many Variables. Ukrainian Math. J. 2018, 70 (2), 252-265. https://doi.org/10.1007/s11253-018-1499-7
$\hspace{75mm} \normalsize{2017}$
• Romanyuk A.S. Trigonometric and Linear Widths for the Classes of Periodic Multivariate Functions. Ukr. Math. J. 2017, 69 (5), 782–795. https://doi.org/10.1007/s11253-017-1395-6
• Romanyuk A.S. Entropy Numbers and Widths for the Classes $B^{r}_{p,\theta}$ of Periodic Functions of Many Variables. Ukr. Math. J. 2017, 68 (10), 1620–1636 (2017).
https://doi.org/10.1007/s11253-017-1315-9
• Romanyuk A.S., Romanyuk V.S. Estimation of the Best Linear Approximations for the Classes $B^{r}_{p,\theta}$ and Singular Numbers of the Integral Operators. Ukr. Math. J. 2017, 68(9), 1424–1436.
https://doi.org/10.1007/s11253-017-1304-z
$\hspace{75mm} \normalsize{2016}$
• Romanyuk A.S. Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables. Ukr. Math. J. 2016, 67 (11), 1739–1757.
https://doi.org/10.1007/s11253-016-1186-5
$\hspace{75mm} \normalsize{2014}$
• Romanyuk A.S. On the Problem of Linear Widths of the Classes $B^{r}_{p,\theta}$ of Periodic Functions of Many Variables. Ukr. Math. J. 2014, 66 (7), 1085–1098. https://doi.org/10.1007/s11253-014-0996-6
• Romanyuk A.S., Romanyuk V.S. Best Bilinear Approximations for the Classes of Functions of Many Variables. Ukr Math J 65 (12), 1862–1882 (2014). https://doi.org/10.1007/s11253-014-0903-1
$\hspace{75mm} \normalsize{2013}$
• Romanyuk, A.S. Best trigonometric and bilinear approximations of classes of functions of several variables. Math Notes 94, 379–391 (2013). https://doi.org/10.1134/S0001434613090095
$\hspace{75mm} \normalsize{2012}$
• Romanyuk A.S., Romanyuk, V.S. Best bilinear approximations of functions from Nikol’skii–Besov classes. Ukr. Math. J. 2012, 64 (5), 781–796 (2012). https://doi.org/10.1007/s11253-012-0678-1
$\hspace{75mm} \normalsize{2011}$
• Romanyuk A. S. Diameters and best approximation of the classes $B^{r}_{p,\theta}$ of periodic functions of several variables. Anal. Math. 2011, 37, 181–213. https://doi.org/10.1007/s10476-011-0303-9
• Romanyuk A. S., Romanyuk V. S. Bilinear approximations of the classes $B^r_{p,\theta}$ of periodic multivariate functions // Math. Analysis, Differential equations and applications. Sofia: Academic Publishing House "Prof. Harin Drinov" – 2011., P. 139 - 148.
$\normalsize{ \textbf{Selected Publications until 2010}}$
- Best approximations and width of classes of periodic functions of several variables // Math. sb. - 2008. - Vol.198, ¹2. - P.93-114.
- Best trigonometric approximations for same classes of periodic functions of several variables in the uniform metric // Math. Notes. - 2007. - Vol.82, ¹2. - P.247-261.
- Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes $B^r_{p,\theta}$ // Izvestiya: Math. - 2006. - Vol. 70, ¹2. - P.69-98.
- Best Kolmogorov and trigonometric widths of the Besov classes $B^r_{p,\theta}$ of multivariate periodic functions // Math. sb. - 2006. - Vol.197, ¹1. - P.71-96.
- Approximation of the classes $B^r_{p,\theta}$ of periodic functions of several variables by liner methods and best approximations // Math. sb. - 2004. - Vol.195, ¹2. - P.237-261.
- Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables // Izvestiya: Math. - 2003. - Vol. 67, ¹2. - P.265-302.
- Approximation of classes of periodic functions of several variables // Math. Notes. - 2002. - Vol.71, ¹1. - P.98-109.
- On estimates of the Kolmogorov widths of the classes $B^r_{p,\theta}$ in the space$L_q$ // Ukrain. Math. J. - 2001. - Vol.53, ¹7. - P.1189-1196.
- On estimates of approximation characteristics of the Besov classes of periodic functions of many variables // Ukrain. Math. J. - 1997. - Vol.49, ¹9. - P.1409-1422.
- The best trigonometric approimations and the Kolmogorov diameters of the Besov classes of functions of mane variables // Ukrain. Math. J. - 1993. - Vol.45, ¹5. - P.724-738.
- Approximation of the Besov classes of periodic function of several variables in a space $L_q$ // Ukrain. Math. J. - 1991. - Vol.43, ¹1. - P.1297-1306.
• Pozharska K., Romanyuk A. The best m-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$. Researches in Mathematics, 2024, 32 (2), 137-154.
https://vestnmath.dnu.dp.ua/index.php/rim/article/view/438
• Pozharska K., Romanyuk A., Romanyuk V. Widths and entropy numbers of the classes of periodic functions of one and several variables in the space $B_{q,1}$. Carpathian Math. Publ. 2024, 16 (2), 351–366.
https://doi.org/10.15330/cmp.16.2.351-366
• Pozharska K., Romanyuk A., Yanchenko S. Best approximations for classes of periodic functions of many variables with bounded dominating mixed derivative. Ukr. Math. J. 2024, 76 (7), 1144–1162; Translated from Ukrains’kyi Matematychnyi Zhurnal 2024, Vol. 76 (7), 1007-1023.
https://doi.org/10.1007/s11253-024-02378-9
$\hspace{75mm} \normalsize{2023}$
• Romanyuk A.S., Romanyuk V.S., Pozharska K.V., Hembars’ka S.B.Characteristics of linear and nonlinear approximation of isotropic classes of periodic multivariate functions. Carpathian Math. Publ. 2023, 15 (1), 78–94.
https://doi.org/10.15330/cmp.15.1.78-94
• Romanyuk A.S., Yanchenko S.Ya. Estimates for the entropy numbers of the Nikol'skii–Besov classes of functions with mixed smoothness in the space of quasi-continuous functions. Math. Nachr. 2023, Vol. 296 (6), 2575–2587.
https://onlinelibrary.wiley.com/doi/10.1002/mana.202100202
$\hspace{75mm} \normalsize{2022}$
• Romanyuk A.S., Yanchenko S.Ya. Approximation of the classes of periodic functions of one and many variables from the Nikol’skii-Besov and Sobolev spaces. Ukrainian Math. J. 2022, Vol. 74 (6), 967-980; Translated from Ukrains’kyi Matematychnyi Zhurnal 2022, Vol. 74 (6), 844-855.
https://link.springer.com/article/10.1007/s11253-022-02110-5
• Romanyuk A.S., Yanchenko S.Ya. Kolmogorov widths of the Nikol'skii-Besov classes of periodic functions of many variables in the space of quasicontinuous functions. Ukr. Math. J. 2022, V. 74, Issue 2, pp. 251–265; Translated from Ukrains’kyi Matematychnyi Zhurnal, V. 74, No. 2, pp. 220–232, February 2022.
https://link.springer.com/article/10.1007/s11253-022-02061-x
• Romanyuk A.S., Yanchenko S.Ya. Estimates of approximating characteristics and the properties of the operators of best approximation for the classes of periodic functions in the space $B_{1,1}$. Ukr. Math. J. February 2022, V. 73, Issue 8, pp. 1278–1298; Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, No. 8, pp. 1102–1119, August, 2021.
https://link.springer.com/article/10.1007/s11253-022-01990-x
$\hspace{75mm} \normalsize{2021}$
• Romanyuk A.S., Romanyuk V.S. Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol’skii–Besov spaces. J. Math. Sci. 2021, 252 (4), 508–525.
https://doi.org/10.1007/s10958-020-05177-2
$\hspace{75mm} \normalsize{2020}$
• Romanyuk A.S., Romanyuk V.S. Estimation of Some Approximating Characteristics of the Classes of Periodic Functions of One and Many Variables. Ukrainian Math. J. 2020, 71 (8), 1257-1272.
https://doi.org/10.1007/s11253-019-01711-x
$\hspace{75mm} \normalsize{2019}$
• Romanyuk A.S. Entropy numbers and widths for the Nikol’skii - Besov classes of functions of many variables in the space $L_{\infty}$. Anal. Math. 2019, 45 (1), 133–151. https://doi.org/10.1007/s10476-018-0611-4
• Romanyuk A.S., Romanyuk V.S. Approximating Characteristics of the Classes of Periodic Multivariate Functions in the Space $B_{\infty,1}$. Ukrainian Math. J., 2019, V. 71, Issue 2, 308-321. https://doi.org/10.1007/s11253-019-01646-3
$\hspace{75mm} \normalsize{2018}$
• Romanyuk A.S. Kolmogorov Widths and Bilinear Approximations of the Classes of Periodic Functions of One and Many Variables. Ukrainian Math. J. 2018, 70 (2), 252-265. https://doi.org/10.1007/s11253-018-1499-7
$\hspace{75mm} \normalsize{2017}$
• Romanyuk A.S. Trigonometric and Linear Widths for the Classes of Periodic Multivariate Functions. Ukr. Math. J. 2017, 69 (5), 782–795. https://doi.org/10.1007/s11253-017-1395-6
• Romanyuk A.S. Entropy Numbers and Widths for the Classes $B^{r}_{p,\theta}$ of Periodic Functions of Many Variables. Ukr. Math. J. 2017, 68 (10), 1620–1636 (2017).
https://doi.org/10.1007/s11253-017-1315-9
• Romanyuk A.S., Romanyuk V.S. Estimation of the Best Linear Approximations for the Classes $B^{r}_{p,\theta}$ and Singular Numbers of the Integral Operators. Ukr. Math. J. 2017, 68(9), 1424–1436.
https://doi.org/10.1007/s11253-017-1304-z
$\hspace{75mm} \normalsize{2016}$
• Romanyuk A.S. Estimation of the Entropy Numbers and Kolmogorov Widths for the Nikol’skii–Besov Classes of Periodic Functions of Many Variables. Ukr. Math. J. 2016, 67 (11), 1739–1757.
https://doi.org/10.1007/s11253-016-1186-5
$\hspace{75mm} \normalsize{2014}$
• Romanyuk A.S. On the Problem of Linear Widths of the Classes $B^{r}_{p,\theta}$ of Periodic Functions of Many Variables. Ukr. Math. J. 2014, 66 (7), 1085–1098. https://doi.org/10.1007/s11253-014-0996-6
• Romanyuk A.S., Romanyuk V.S. Best Bilinear Approximations for the Classes of Functions of Many Variables. Ukr Math J 65 (12), 1862–1882 (2014). https://doi.org/10.1007/s11253-014-0903-1
$\hspace{75mm} \normalsize{2013}$
• Romanyuk, A.S. Best trigonometric and bilinear approximations of classes of functions of several variables. Math Notes 94, 379–391 (2013). https://doi.org/10.1134/S0001434613090095
$\hspace{75mm} \normalsize{2012}$
• Romanyuk A.S., Romanyuk, V.S. Best bilinear approximations of functions from Nikol’skii–Besov classes. Ukr. Math. J. 2012, 64 (5), 781–796 (2012). https://doi.org/10.1007/s11253-012-0678-1
$\hspace{75mm} \normalsize{2011}$
• Romanyuk A. S. Diameters and best approximation of the classes $B^{r}_{p,\theta}$ of periodic functions of several variables. Anal. Math. 2011, 37, 181–213. https://doi.org/10.1007/s10476-011-0303-9
• Romanyuk A. S., Romanyuk V. S. Bilinear approximations of the classes $B^r_{p,\theta}$ of periodic multivariate functions // Math. Analysis, Differential equations and applications. Sofia: Academic Publishing House "Prof. Harin Drinov" – 2011., P. 139 - 148.
$\normalsize{ \textbf{Selected Publications until 2010}}$
- Best approximations and width of classes of periodic functions of several variables // Math. sb. - 2008. - Vol.198, ¹2. - P.93-114.
- Best trigonometric approximations for same classes of periodic functions of several variables in the uniform metric // Math. Notes. - 2007. - Vol.82, ¹2. - P.247-261.
- Bilinear and trigonometric approximations of periodic functions of several variables of Besov classes $B^r_{p,\theta}$ // Izvestiya: Math. - 2006. - Vol. 70, ¹2. - P.69-98.
- Best Kolmogorov and trigonometric widths of the Besov classes $B^r_{p,\theta}$ of multivariate periodic functions // Math. sb. - 2006. - Vol.197, ¹1. - P.71-96.
- Approximation of the classes $B^r_{p,\theta}$ of periodic functions of several variables by liner methods and best approximations // Math. sb. - 2004. - Vol.195, ¹2. - P.237-261.
- Best $M$-term trigonometric approximations of Besov classes of periodic functions of several variables // Izvestiya: Math. - 2003. - Vol. 67, ¹2. - P.265-302.
- Approximation of classes of periodic functions of several variables // Math. Notes. - 2002. - Vol.71, ¹1. - P.98-109.
- On estimates of the Kolmogorov widths of the classes $B^r_{p,\theta}$ in the space$L_q$ // Ukrain. Math. J. - 2001. - Vol.53, ¹7. - P.1189-1196.
- On estimates of approximation characteristics of the Besov classes of periodic functions of many variables // Ukrain. Math. J. - 1997. - Vol.49, ¹9. - P.1409-1422.
- The best trigonometric approimations and the Kolmogorov diameters of the Besov classes of functions of mane variables // Ukrain. Math. J. - 1993. - Vol.45, ¹5. - P.724-738.
- Approximation of the Besov classes of periodic function of several variables in a space $L_q$ // Ukrain. Math. J. - 1991. - Vol.43, ¹1. - P.1297-1306.