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. F.; Polyakov, O. V. On the nonsymmetric approximation of continuous functions in the integral metric. (English) Zbl 1489.41006 Res. Math. 27, No. 2, 7-12 (2019). MSC: 41A20 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{O. V. Polyakov}, Res. Math. 27, No. 2, 7--12 (2019; Zbl 1489.41006) Full Text: DOI OA License
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, V. F.; Parfinovich, N. V. On the order of relative approximation of classes of differentiable periodic functions by splines. (Russian, English) Zbl 1224.41035 Ukr. Mat. Zh. 62, No. 2, 147-157 (2010); translation in Ukr. Math. J. 62, No. 2, 163-174 (2010). MSC: 41A15 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{N. V. Parfinovich}, Ukr. Mat. Zh. 62, No. 2, 147--157 (2010; Zbl 1224.41035); translation in Ukr. Math. J. 62, No. 2, 163--174 (2010)
Babenko, V. F.; Parfinovich, N. V. Nonsymmetric approximations of classes of periodic functions by splines of defect 2 and Jackson-type inequalities. (Russian, English) Zbl 1224.41034 Ukr. Mat. Zh. 61, No. 11, 1443-1454 (2009); translation in Ukr. Math. J. 61, No. 11, 1695-1709 (2009). MSC: 41A15 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{N. V. Parfinovich}, Ukr. Mat. Zh. 61, No. 11, 1443--1454 (2009; Zbl 1224.41034); translation in Ukr. Math. J. 61, No. 11, 1695--1709 (2009) Full Text: DOI
Babenko, V. F.; Parfinovich, N. V. Exact values of best approximations for classes of periodic functions by splines of deficiency 2. (English. Russian original) Zbl 1204.41018 Math. Notes 85, No. 4, 515-527 (2009); translation from Mat. Zametki 85, No. 4, 538-551 (2009). Reviewer: Kai Diethelm (Braunschweig) MSC: 41A44 41A50 41A15 41A46 65D07 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{N. V. Parfinovich}, Math. Notes 85, No. 4, 515--527 (2009; Zbl 1204.41018); translation from Mat. Zametki 85, No. 4, 538--551 (2009) Full Text: DOI
Babenko, V. F.; Borodachov, S. V. On optimization of approximate integration over \(d\)-dimensional ball. (English) Zbl 1111.41021 East J. Approx. 9, No. 1, 95-109 (2003). MSC: 41A50 41A30 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{S. V. Borodachov}, East J. Approx. 9, No. 1, 95--109 (2003; Zbl 1111.41021)
Babenko, V. F.; Britvin, Y. E. On Kolmogorov’s problem about existence of a function with given norms of its derivatives. (English) Zbl 1145.41309 East J. Approx. 8, No. 1, 95-110 (2002). MSC: 41A50 41A17 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{Y. E. Britvin}, East J. Approx. 8, No. 1, 95--110 (2002; Zbl 1145.41309)
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. On Kolmogorov-type inequalities with integrable higher derivatives. (Ukrainian. English summary) Zbl 1025.26011 Ukr. Mat. Zh. 54, No. 12, 1694-1697 (2002). MSC: 26D10 41A17 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 54, No. 12, 1694--1697 (2002; Zbl 1025.26011) Full Text: DOI
Babenko, V. F.; Gorbenko, M. E. On the uniqueness of an element of the best \(L_1\)-approximation for functions with values in a Banach space. (English. Russian original) Zbl 0978.41018 Ukr. Math. J. 52, No. 1, 29-34 (2000); translation from Ukr. Mat. Zh. 52, No. 1, 30-34 (2000). MSC: 41A50 41A65 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{M. E. Gorbenko}, Ukr. Mat. Zh. 52, No. 1, 30--34 (2000; Zbl 0978.41018); translation from Ukr. Mat. Zh. 52, No. 1, 30--34 (2000) Full Text: DOI
Babenko, V. F.; Parfinovich, N. V. On the best \(L_1\)-approximations of functional classes by splines under restrictions imposed on their derivatives. (English. Russian original) Zbl 0957.41020 Ukr. Math. J. 51, No. 4, 481-491 (1999); translation from Ukr. Mat. Zh. 51, No. 4, 435-444 (1999). MSC: 41A50 41A15 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{N. V. Parfinovich}, Ukr. Mat. Zh. 51, No. 4, 435--444 (1999; Zbl 0957.41020); translation from Ukr. Mat. Zh. 51, No. 4, 435--444 (1999)
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Landau-Kolmogorov-Hörmander inequalities on the semiaxis. (English. Russian original) Zbl 0961.41010 Math. Notes 65, No. 2, 144-152 (1999); translation from Mat. Zametki 65, No. 2, 175-185 (1999). Reviewer: Boris Rubin (Jerusalem) MSC: 41A17 26D10 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Math. Notes 65, No. 2, 144--152 (1999; Zbl 0961.41010); translation from Mat. Zametki 65, No. 2, 175--185 (1999) Full Text: DOI
Babenko, V. F.; Leis, Azar The best \(L_1\)-approximations of classes of functions defined by differential operators in terms of generalized splines from these classes. (English. Russian original) Zbl 0942.41004 Ukr. Math. J. 50, No. 11, 1649-1658 (1998); translation from Ukr. Mat. Zh. 50, No. 11, 1443-1451 (1998). MSC: 41A15 41A35 41A10 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{A. Leis}, Ukr. Mat. Zh. 50, No. 11, 1443--1451 (1998; Zbl 0942.41004); translation from Ukr. Mat. Zh. 50, No. 11, 1443--1451 (1998) Full Text: DOI
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Comparison of approximation properties of generalized polynomials and splines. (English. Russian original) Zbl 0946.41016 Ukr. Math. J. 50, No. 8, 1151-1161 (1998); translation from Ukr. Mat. Zh. 50, No. 8, 1011-1020 (1998). MSC: 41A50 41A15 42A10 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Ukr. Mat. Zh. 50, No. 8, 1011--1020 (1998; Zbl 0946.41016); translation from Ukr. Mat. Zh. 50, No. 8, 1011--1020 (1998) Full Text: DOI
Babenko, V. F.; Azar, L.; Parfinovich, N. V. On approximation of classes of periodic functions by splines under restrictions on derivatives. (Russian) Zbl 0974.41502 Samoilenko, A. M. (ed.) et al., Fourier series: Theory and applications. Section: Function theory. Kyïv: Instytut Matematyky NAN Ukraïny. Pr. Inst. Mat. Nats. Akad. Nauk Ukr., Mat. Zastos. 20, 18-29 (1998). Reviewer: Alexander Gomilko (Kyïv) MSC: 41A15 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., in: Ryady Fur'eh: Teoriya i zastosuvannya. Sektsiya: Teoriya funktsij. Kyïv: Instytut Matematyky NAN Ukraïny. 18--29 (1998; Zbl 0974.41502)
Babenko, V. F.; Polyakov, O. V.; Traktinskaya, V. N. The dimension of the polyhedra of the best \(L_1\)-approximation. (English. Russian original) Zbl 0957.41022 Dokl. Math. 56, No. 3, 891-893 (1997); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 357, No. 4, 439-441 (1997). MSC: 41A50 41A30 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., Dokl. Math. 56, No. 3, 439--441 (1997; Zbl 0957.41022); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 357, No. 4, 439--441 (1997)
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. Inequalities for norms of intermediate derivatives of periodic functions and their applications. (English) Zbl 0920.26013 East J. Approx. 3, No. 3, 351-376 (1997). Reviewer: D.Dryanov (Sofia) MSC: 26D10 41A17 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., East J. Approx. 3, No. 3, 351--376 (1997; Zbl 0920.26013)
Babenko, V. F.; Polyakov, O. V.; Tractinskaya, V. N. On Chebyshev rank in \(L_1\)-approximation. (English) Zbl 0893.41017 East J. Approx. 3, No. 1, 39-61 (1997). Reviewer: D.Dryanov (Sofia) MSC: 41A52 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} et al., East J. Approx. 3, No. 1, 39--61 (1997; Zbl 0893.41017)
Babenko, V. F.; Polyakov, O. V. Approximations on average of certain classes of continuous periodic functions. (English. Russian original) Zbl 0851.42002 Russ. Math. 39, No. 2, 10-18 (1995); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1995, No. 2(393), 13-21 (1995). Reviewer: S.M.Mazhar (Kuwait) MSC: 42A10 41A15 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{O. V. Polyakov}, Russ. Math. 39, No. 2, 13--21 (1995; Zbl 0851.42002); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1995, No. 2(393), 13--21 (1995)
Babenko, V. F.; Glushko, V. N. On the uniqueness of elements of the best approximation and the best one-sided approximation in the space \(L_ 1\). (English. Russian original) Zbl 0845.41019 Ukr. Math. J. 46, No. 5, 503-513 (1994); translation from Ukr. Mat. Zh. 46, No. 5, 475-483 (1994). Reviewer: I.Serb (Cluj-Napoca) MSC: 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{V. N. Glushko}, Ukr. Mat. Zh. 46, No. 5, 475--483 (1994; Zbl 0845.41019); translation from Ukr. Mat. Zh. 46, No. 5, 475--483 (1994) Full Text: DOI
Babenko, V. F. The best \(L_ 1\)-approximations by splines in the presence of restrictions on their derivatives. (English. Russian original) Zbl 0848.42004 Math. Notes 51, No. 5, 432-437 (1992); translation from Mat. Zametki 51, No. 5, 12-19 (1992). Reviewer: W.Łenski (Poznań) MSC: 42A10 41A15 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko}, Math. Notes 51, No. 5, 1 (1992; Zbl 0848.42004); translation from Mat. Zametki 51, No. 5, 12--19 (1992) Full Text: DOI
Babenko, V. F.; Shalaev, V. V. Best approximation estimates resulting from the Chebyshev criterion. (English. Russian original) Zbl 0753.42001 Math. Notes 49, No. 4, 431-433 (1991); translation from Mat. Zametki 49, No. 4, 148-150 (1991). MSC: 42A10 41A17 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{V. V. Shalaev}, Math. Notes 49, No. 4, 431--433 (1991; Zbl 0753.42001); translation from Mat. Zametki 49, No. 4, 148--150 (1991) Full Text: DOI
Babenko, V. F.; Ligun, A. A. Development of studies on the exact solution of extremal problems of the theory of best approximation. (English. Russian original) Zbl 0729.41028 Ukr. Math. J. 42, No. 1, 1-13 (1990); translation from Ukr. Mat. Zh. 42, No. 1, 4-17 (1990). MSC: 41A50 41A65 41A46 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{A. A. Ligun}, Ukr. Math. J. 42, No. 1, 1--13 (1990; Zbl 0729.41028); translation from Ukr. Mat. Zh. 42, No. 1, 4--17 (1990) Full Text: DOI
Babenko, V. F.; Ligun, A. A. Development of studies on the exact solution of extremal problems of the theory of best approximation. (English. Russian original) Zbl 0715.41038 Ukr. Math. J. 42, No. 1, 1-13 (1990); translation from Ukr. Mat. Zh. 42, No. 1, 4-17 (1990). MSC: 41A50 41A65 41A46 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{A. A. Ligun}, Ukr. Math. J. 42, No. 1, 1--13 (1990; Zbl 0715.41038); translation from Ukr. Mat. Zh. 42, No. 1, 4--17 (1990) Full Text: DOI
Babenko, V. F. Approximations in the mean in the presence of constraints upon the derivatives of approximating functions. (Russian) Zbl 0725.41021 Questions of analysis and approximation, Collect. Sci. Works, Kiev, 9-18 (1989). MSC: 41A50 41A65 PDFBibTeX XML
Babenko, V. F. Nonsymetric approximations and inequalities for rearrangements in extremal problems of approximation theory. (English) Zbl 0709.41505 Proc. Steklov Inst. Math. 180, 35-37 (1989). MSC: 41A17 41A50 46E30 PDFBibTeX XMLCite \textit{V. F. Babenko}, Proc. Steklov Inst. Math. 180, 35--37 (1989; Zbl 0709.41505)
Babenko, V. F. Approximation of function classes defined by means of a modulus of continuity. (English. Russian original) Zbl 0702.41028 Sov. Math., Dokl. 37, No. 1, 239-241 (1988); translation from Dokl. Akad. Nauk SSSR 298, No. 6, 1296-1299 (1988). Reviewer: G.D.Dikshit MSC: 41A30 41A35 41A46 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko}, Sov. Math., Dokl. 37, No. 1, 239--241 (1988; Zbl 0702.41028); translation from Dokl. Akad. Nauk SSSR 298, No. 6, 1296--1299 (1988)
Babenko, V. F. Some exact inequalities for approximations of periodic functions in the space \(L_ 1\). (Russian) Zbl 0683.42001 Studies on modern problems of summation and approximation of functions and their applications, Collect. Sci. Works, 4-6 (1987). MSC: 42A05 41A50 PDFBibTeX XML
Babenko, V. F. Extremal problems in approximation theory, and inequalities for rearrangements. (English. Russian original) Zbl 0642.41019 Sov. Math., Dokl. 34, 369-372 (1987); translation from Dokl. Akad. Nauk SSSR 290, 1033-1036 (1986). Reviewer: P.Achuthan MSC: 41A50 41A46 41A17 PDFBibTeX XMLCite \textit{V. F. Babenko}, Sov. Math., Dokl. 34, 369--372 (1987; Zbl 0642.41019); translation from Dokl. Akad. Nauk SSSR 290, 1033--1036 (1986)
Babenko, V. F.; Kofanov, V. A. Polynomials of fixed sign that deviate least from zero in the spaces \(L_ p\). (English. Russian original) Zbl 0581.41009 Math. Notes 37, 99-105 (1985); translation from Mat. Zametki 37, No. 2, 176-185 (1985). Reviewer: L.A.Čantunja MSC: 41A10 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{V. A. Kofanov}, Math. Notes 37, 99--105 (1985; Zbl 0581.41009); translation from Mat. Zametki 37, No. 2, 176--185 (1985) Full Text: DOI
Babenko, V. F. Nonsymmetric extremal problems in approximation theory. (English. Russian original) Zbl 0568.41032 Sov. Math., Dokl. 27, 346-349 (1983); translation from Dokl. Akad. Nauk SSSR 269, No. 3, 521-524 (1983). Reviewer: G.Zhang MSC: 41A65 41A50 42A10 PDFBibTeX XMLCite \textit{V. F. Babenko}, Sov. Math., Dokl. 27, 346--349 (1983; Zbl 0568.41032); translation from Dokl. Akad. Nauk SSSR 269, No. 3, 521--524 (1983)
Babenko, V. F. Nonsymmetric approximation in spaces of integrable functions. (English. Russian original) Zbl 0522.41028 Ukr. Math. J. 34, 331-336 (1983); translation from Ukr. Mat. Zh. 34, 409-416 (1982). MSC: 41A65 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko}, Ukr. Math. J. 34, 331--336 (1983; Zbl 0522.41028); translation from Ukr. Mat. Zh. 34, 409--416 (1982) Full Text: DOI
Babenko, V. F.; Pichugov, S. A. Approximation in the mean of linear combinations of shifts of certain functions. (English. Russian original) Zbl 0499.41017 Ukr. Math. J. 33, 182-186 (1981); translation from Ukr. Mat. Zh. 33, 234-240 (1981). MSC: 41A45 42A85 41A50 42A10 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{S. A. Pichugov}, Ukr. Math. J. 33, 182--186 (1981; Zbl 0499.41017); translation from Ukr. Mat. Zh. 33, 234--240 (1981) Full Text: DOI
Babenko, V. F.; Pichugov, S. A. A remark to the A. N. Kolmogorov inequality. (Russian) Zbl 0475.41014 Investigations on modern problems of summation and approximation of functions and their applications, Collect. sci. Works, Dnepropetrovsk 1980, 14-17 (1980). MSC: 41A17 41A50 PDFBibTeX XML
Babenko, V. F.; Pichugov, S. A. Asymptotic properties of the best uniform approximation of periodic functions. (Russian) Zbl 0473.42003 Investigations on modern problems of summation and approximation of functions and their applications, Collect. sci. Works, Dnepropetrovsk 1980, 10-14 (1980). MSC: 42A10 41A50 41A10 PDFBibTeX XML
Babenko, V. F.; Ligun, A. A. On the best one-sided approximations by trigonometric polynomials and splines. (Russian) Zbl 0511.41006 Investigations on modern problems of summation and approximation of functions and their applications, Collect. sci. Works, Dnepropetrovsk 1979, 6-9 (1979). MSC: 41A15 42A10 41A50 PDFBibTeX XML
Babenko, V. F.; Ligun, A. A. The order of the best one-sided approximation by polynomials and splines in the \(L_p\)-metric. (English) Zbl 0348.41019 Math. Notes 19, 194-198 (1976). MSC: 41A25 41A15 41A65 41A10 41A50 42A10 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{A. A. Ligun}, Math. Notes 19, 194--198 (1976; Zbl 0348.41019) Full Text: DOI
Babenko, V. F.; Ligun, A. A. Die Ordnung der besten einseitigen Approximationen vermittels Polynome und Splinefunktionen in der \(L_p\)-Metrik. (Russian) Zbl 0341.41016 Mat. Zametki 19, 323-329 (1976). MSC: 41A25 41A10 41A15 41A50 41A65 42A10 PDFBibTeX XMLCite \textit{V. F. Babenko} and \textit{A. A. Ligun}, Mat. Zametki 19, 323--329 (1976; Zbl 0341.41016)
Babenko, V. F. Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions. (English. Russian original) Zbl 0333.41024 Math. Notes 19, 187-193 (1976); translation from Mat. Zametki 19, 313-322 (1976). MSC: 41A55 41A50 PDFBibTeX XMLCite \textit{V. F. Babenko}, Math. Notes 19, 187--193 (1976; Zbl 0333.41024); translation from Mat. Zametki 19, 313--322 (1976) Full Text: DOI