Babenko, Vladyslav; Babenko, Vira; Kovalenko, Oleg Korneichuk-Stechkin lemma, Ostrowski and Landau inequalities, and optimal recovery problems for \(L\)-space valued functions. (English) Zbl 07739381 Numer. Funct. Anal. Optim. 44, No. 12, 1309-1341 (2023). MSC: 41A65 41A17 46E40 41A44 PDFBibTeX XMLCite \textit{V. Babenko} et al., Numer. Funct. Anal. Optim. 44, No. 12, 1309--1341 (2023; Zbl 07739381) Full Text: DOI arXiv
Babenko, Vladyslav; Kovalenko, Oleg; Parfinovych, Nataliia On approximation of hypersingular integral operators by bounded ones. (English) Zbl 1505.41002 J. Math. Anal. Appl. 513, No. 2, Article ID 126215, 21 p. (2022). Reviewer: Alexei Lukashov (Moskva) MSC: 41A17 26D99 47A58 PDFBibTeX XMLCite \textit{V. Babenko} et al., J. Math. Anal. Appl. 513, No. 2, Article ID 126215, 21 p. (2022; Zbl 1505.41002) Full Text: DOI arXiv
Babenko, V. F.; Parfinovych, N. V.; Skorokhodov, D. S. Optimal recovery of operator sequences. (English) Zbl 1502.41008 Mat. Stud. 56, No. 2, 193-207 (2021). MSC: 41A50 46A45 47N10 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Mat. Stud. 56, No. 2, 193--207 (2021; Zbl 1502.41008) Full Text: DOI arXiv
Babenko, V.; Babenko, Yu.; Kriachko, N.; Skorokhodov, D. On Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces. (English) Zbl 1495.47035 Anal. Math. 47, No. 4, 709-745 (2021). MSC: 47A63 41A35 26D10 41A65 PDFBibTeX XMLCite \textit{V. Babenko} et al., Anal. Math. 47, No. 4, 709--745 (2021; Zbl 1495.47035) Full Text: DOI arXiv
Babenko, V. F.; Parfinovich, N. V. Estimation of the uniform norm of one-dimensional Riesz potential of the partial derivative of a function with bounded Laplacian. (English. Russian original) Zbl 1499.42045 Ukr. Math. J. 68, No. 7, 987-999 (2016); translation from Ukr. Mat. Zh. 68, No. 7, 867-878 (2016). MSC: 42B08 35B45 35B65 35J25 31B35 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{N. V. Parfinovich}, Ukr. Math. J. 68, No. 7, 987--999 (2016; Zbl 1499.42045); translation from Ukr. Mat. Zh. 68, No. 7, 867--878 (2016) Full Text: DOI
Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V. On the optimal recovery of integrals of set-valued functions. (English) Zbl 1386.41010 Ukr. Math. J. 67, No. 9, 1306-1315 (2016) and Ukr. Mat. Zh. 67, No. 9, 1163-1171 (2015). MSC: 41A55 41A50 41A65 65D32 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Math. J. 67, No. 9, 1306--1315 (2016; Zbl 1386.41010) Full Text: DOI arXiv
Babenko, Vladyslav; Babenko, Yuliya; Kriachko, Nadiia Inequalities of Hardy-Littlewood-Pólya type for functions of operators and their applications. (English) Zbl 1350.26002 J. Math. Anal. Appl. 444, No. 1, 512-526 (2016). Reviewer: Vijay Gupta (New Delhi) MSC: 26A15 41A36 PDFBibTeX XMLCite \textit{V. Babenko} et al., J. Math. Anal. Appl. 444, No. 1, 512--526 (2016; Zbl 1350.26002) Full Text: DOI arXiv
Babenko, Vladyslav; Babenko, Yuliya; Parfinovych, Nataliia; Skorokhodov, Dmytro Optimal recovery of integral operators and its applications. (English) Zbl 1416.65563 J. Complexity 35, 102-123 (2016). MSC: 65R32 65R20 45Q05 PDFBibTeX XMLCite \textit{V. Babenko} et al., J. Complexity 35, 102--123 (2016; Zbl 1416.65563) Full Text: DOI arXiv
Babenko, Vladislav F.; Kovalenko, Oleg V. On modulus of continuity of differentiation operator on weighted Sobolev classes. (English) Zbl 1391.26040 J. Inequal. Appl. 2015, Paper No. 295, 16 p. (2015). MSC: 26D10 41A17 46E35 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{O. V. Kovalenko}, J. Inequal. Appl. 2015, Paper No. 295, 16 p. (2015; Zbl 1391.26040) Full Text: DOI arXiv
Babenko, Vladyslav; Babenko, Yuliya; Kovalenko, Oleg Kolmogorov’s problem on the class of multiply monotone functions. (English) Zbl 1325.41007 Adv. Math. 280, 256-281 (2015). Reviewer: Yuri A. Farkov (Moscow) MSC: 41A17 41A10 26D10 41A30 41A44 PDFBibTeX XMLCite \textit{V. Babenko} et al., Adv. Math. 280, 256--281 (2015; Zbl 1325.41007) Full Text: DOI arXiv
Babenko, Vladislav F.; Churilova, Mariya S.; Parfinovych, Nataliia V.; Skorokhodov, Dmytro S. Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line. (English) Zbl 1336.26021 J. Inequal. Appl. 2014, Paper No. 504, 29 p. (2014). MSC: 26D10 26A33 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., J. Inequal. Appl. 2014, Paper No. 504, 29 p. (2014; Zbl 1336.26021) Full Text: DOI arXiv
Babenko, V. F.; Parfinovich, N. V.; Pichugov, S. A. Kolmogorov-type inequalities for norms of Riesz derivatives of functions of several variables with Laplacian bounded in \(L_\infty\) and related problems. (English. Russian original) Zbl 1314.41006 Math. Notes 95, No. 1, 3-14 (2014); translation from Mat. Zametki 95, No. 1, 3-17 (2014). MSC: 41A17 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Math. Notes 95, No. 1, 3--14 (2014; Zbl 1314.41006); translation from Mat. Zametki 95, No. 1, 3--17 (2014) Full Text: DOI
Babenko, V. F.; Parfinovich, N. V. Kolmogorov type inequalities for norms of Riesz derivatives of multivariate functions and some applications. (English. Russian original) Zbl 1304.41008 Proc. Steklov Inst. Math. 277, Suppl. 1, S9-S20 (2012); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 17, No. 3, 60-70 (2011). Reviewer: Alexei Lukashov (Istanbul) MSC: 41A17 41A35 41A36 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{N. V. Parfinovich}, Proc. Steklov Inst. Math. 277, S9--S20 (2012; Zbl 1304.41008); translation from Tr. Inst. Mat. Mekh. (Ekaterinburg) 17, No. 3, 60--70 (2011) Full Text: DOI
Babenko, Vladislav F.; Parfinovich, Natal’ya V. Inequalities of the Kolmogorov type for norms of Riesz derivatives of multivariate functions and some of their applications. (English. Russian original) Zbl 1271.41004 J. Math. Sci., New York 187, No. 1, 9-21 (2012); translation from Ukr. Mat. Visn. 9, No. 2, 157-174 (2012). Reviewer: D. K. Ugulawa (Tbilisi) MSC: 41A17 26E99 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{N. V. Parfinovich}, J. Math. Sci., New York 187, No. 1, 9--21 (2012; Zbl 1271.41004); translation from Ukr. Mat. Visn. 9, No. 2, 157--174 (2012) Full Text: DOI
Babenko, V. F.; Churilova, M. S. Estimates for the norms of fractional derivatives in terms of integral moduli of continuity and their applications. (English. Russian original) Zbl 1254.26009 Ukr. Math. J. 63, No. 9, 1321-1335 (2012); translation from Ukr. Mat. Zh. 63, No. 9, 1155-1168 (2011). MSC: 26A33 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{M. S. Churilova}, Ukr. Math. J. 63, No. 9, 1321--1335 (2012; Zbl 1254.26009); translation from Ukr. Mat. Zh. 63, No. 9, 1155--1168 (2011) Full Text: DOI
Babenko, V. F.; Zontov, V. A. Bernstein-type inequalities for splines defined on the real axis. (English. Russian original) Zbl 1242.41011 Ukr. Math. J. 63, No. 5, 699-708 (2011); translation from Ukr. Mat. Zh. 63, No. 5, 603-611 (2011). Reviewer: Yuri A. Farkov (Moscow) MSC: 41A17 41A15 41A44 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{V. A. Zontov}, Ukr. Math. J. 63, No. 5, 699--708 (2011; Zbl 1242.41011); translation from Ukr. Mat. Zh. 63, No. 5, 603--611 (2011) Full Text: DOI
Babenko, V. F.; Borodachov, S. V.; Skorokhodov, D. S. Optimal cubature formulas for tensor products of certain classes of functions. (English) Zbl 1231.41029 J. Complexity 27, No. 6, 519-530 (2011). Reviewer: Kai Diethelm (Braunschweig) MSC: 41A55 65D32 41A63 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., J. Complexity 27, No. 6, 519--530 (2011; Zbl 1231.41029) Full Text: DOI
Babenko, V. F.; Ligun, A. A. Bernstein-type inequalities for \(\mathfrak{L}\)-splines. (English. Russian original) Zbl 0805.42002 Ukr. Math. J. 45, No. 1, 8-20 (1993); translation from Ukr. Mat. Zh. 45, No. 1, 10-20 (1993). Reviewer: L.Leindler (Szeged) MSC: 42A05 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{A. A. Ligun}, Ukr. Math. J. 45, No. 1, 8--20 (1993; Zbl 0805.42002); translation from Ukr. Mat. Zh. 45, No. 1, 10--20 (1993) Full Text: DOI