Edit Profile (opens in new tab) Babenko, Vladyslav Fedorovych Co-Author Distance Author ID: babenko.vladislav-f Published as: Babenko, V. F.; Babenko, Vladislav; Babenko, Vladislav F.; Babenko, Vladyslav; Babenko, V. more...less External Links: Google Scholar · ResearchGate · Math-Net.Ru · dblp Documents Indexed: 233 Publications since 1975, including 3 Books and 15 Additional arXiv Preprints Co-Authors: 65 Co-Authors with 187 Joint Publications 1,059 Co-Co-Authors all top 5 Co-Authors 45 single-authored 50 Pichugov, S. A. 33 Kofanov, V. A. 27 Kovalenko, Oleg V. 27 Parfinovych, Nataliia Viktorivna 19 Skorokhodov, Dmytro S. 16 Ligun, A. A. 15 Babenko, Yuliya 10 Babenko, Viktor V. 9 Borodachov, Sergiy V. 8 Polyakov, O. V. 6 Korneĭchuk, Nikolaĭ Pavlovich 5 Babenko, Vira 5 Bilichenko, R. O. 5 Churilova, Mariya S. 5 Motornyĭ, Vitaliĭ Pavlovych 4 Gun’ko, M. S. 4 Rudenko, A. A. 3 Babenko, Yu. V. 3 Konareva, S. V. 3 Kriachko, Nadiia 3 Polishchuk, M. V. 3 Vakarchuk, Mihail B. 2 Glushko, V. N. 2 Gorbenko, M. E. 2 Kofanov, V. O. 2 Leskevych, T. Yu. 2 Levchenko, D. A. 2 Ligun, Anatoliy 2 Pasko, A. M. 2 Rudenko, O. O. 2 Shalaev, V. V. 2 Spektor, Susanna 2 Tkachenko, M. Ye. 2 Traktynska, V. M. 1 Azar, Laith Emil 1 Britvin, Y. E. 1 Churilova, M. G. 1 Doronin, V. G. 1 Dovgoshey, Oleksiy Alfredovich 1 Goncharov, Sergij V. 1 Kofanov, Vladimir 1 Konareva, Svitlana 1 Kozlo, G. V. 1 Kozynenko, O. V. 1 Leis, Azar 1 Leskevich, T. Yu. 1 Mytropol’skyĭ, Yuriĭ Oleksiĭovych 1 Nazarenko, N. A. 1 Nikol’skiĭ, Sergeĭ Mikhaĭlovich 1 Rassias, Themistocles Michael 1 Ruban, V. I. 1 Rybnikova, T. I. 1 Samoĭlenko, Anatoliĭ Mykhaĭlovych 1 Savela, S. V. 1 Selivanova, S. A. 1 Shumeiko, A. A. 1 Shumeiko, Alexander 1 Spector, S. A. 1 Tkachenko, M. E. 1 Tractinskaya, V. N. 1 Traktinskaya, V. N. 1 Uédraogo, Zh. B. 1 Velikin, V. L. 1 Zhiganova, G. S. 1 Zontov, V. A. all top 5 Serials 42 Ukraïns’kyĭ Matematychnyĭ Zhurnal 32 Ukrainian Mathematical Journal 21 East Journal on Approximations 17 Mathematical Notes 9 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 7 Researches in Mathematics 6 Analysis Mathematica 5 Matematicheskie Zametki 5 Journal of Complexity 4 Soviet Mathematics. Doklady 4 Dopovidi Akademiï Nauk Ukraïni 4 Doklady Mathematics 3 Journal of Mathematical Analysis and Applications 3 Proceedings of the Steklov Institute of Mathematics 3 Jaen Journal on Approximation 3 Carpathian Mathematical Publications 2 Numerical Functional Analysis and Optimization 2 Constructive Approximation 2 Modelirovanie v Mekhanike 2 Journal of Inequalities and Applications 2 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 1 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 1 Advances in Mathematics 1 Siberian Mathematical Journal 1 Dopovidi Akademiï Nauk Ukraïns’koï RSR. Seriya A 1 Russian Mathematics 1 Communications in Analysis and Geometry 1 Journal of Mathematical Sciences (New York) 1 Matematychni Studiï 1 Mathematical Inequalities & Applications 1 Trudy Instituta Prikladnoĭ Matematiki i Mekhaniki 1 Banach Journal of Mathematical Analysis all top 5 Fields 179 Approximations and expansions (41-XX) 64 Real functions (26-XX) 47 Harmonic analysis on Euclidean spaces (42-XX) 27 Functional analysis (46-XX) 20 Operator theory (47-XX) 12 Numerical analysis (65-XX) 4 History and biography (01-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Partial differential equations (35-XX) 2 Integral equations (45-XX) 2 Convex and discrete geometry (52-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 132 Publications have been cited 454 times in 229 Documents Cited by ▼ Year ▼ Extremal properties of polynomials and splines. Based on the Russian edition 1992. Zbl 0976.41008 Korneichuk, N. P.; Ligun, A. A.; Babenko, V. F. 47 1996 Comparison of rearrangement and Kolmogorov-Nagy type inequalities for periodic functions. Zbl 1034.41010 Babenko, Vladislav; Kofanov, Vladimir; Pichugov, Sergei 14 2002 Comparison of exact constants in inequalities for derivatives of functions defined on the real axis and a circle. Zbl 1103.26013 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 14 2003 Approximations, widths and optimal quadrature formulae for classes of periodic functions with rearrangements invariant sets of derivatives. Zbl 0652.41008 Babenko, V. F. 13 1987 Multivariate inequalities of Kolmogorov type and their applications. Zbl 0911.46024 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 12 1997 Inequalities of Kolmogorov type and some of their applications in approximation theory. Zbl 0909.41008 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 10 1998 Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions. Zbl 0333.41024 Babenko, V. F. 10 1976 On the optimal error bound for cubature formulae on certain classes of continuous functions. Zbl 0372.41020 Babenko, V. F. 9 1977 On the Kolmogorov type inequalities for fractional derivatives. Zbl 1331.26028 Babenko, V. F.; Churilova, M. G. 8 2002 Sharp estimates of the norms of fractional derivatives of functions of several variables satisfying Hölder conditions. Zbl 1205.26008 Babenko, V. F.; Pichugov, S. A. 8 2010 Kolmogorov-type inequalities for norms of Riesz derivatives of functions of several variables with Laplacian bounded in \(L_\infty\) and related problems. Zbl 1314.41006 Babenko, V. F.; Parfinovich, N. V.; Pichugov, S. A. 8 2014 Optimal recovery of isotropic classes of twice-differentiable multivariate functions. Zbl 1215.41001 Babenko, Vladislav F.; Borodachov, Sergiy V.; Skorokhodov, Dmytro S. 8 2010 Extremal properties of polynomials and splines. (Ehkstremal’nye svojstva polinomov i splajnov.) Zbl 0853.41006 Kornejchuk, N. P.; Babenko, V. F.; Ligun, A. A. 7 1992 Calculus and nonlinear integral equations for functions with values in \(L\)-spaces. Zbl 1449.45009 Babenko, V. 7 2019 Kolmogorov type inequalities for norms of Riesz derivatives of multivariate functions and some applications. Zbl 1304.41008 Babenko, V. F.; Parfinovich, N. V. 7 2012 Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic. Zbl 1131.26010 Babenko, Vladislav F.; Churilova, Mariya S. 6 2007 The exact inequalities of the Kolmogorov type for functions of two variables. Zbl 1054.41503 Babenko, V. F. 6 2000 Investigations of Dnepropetrovsk mathematicians related to inequalities for derivatives of periodic functions and their applications. Zbl 0976.41001 Babenko, V. F. 6 2000 Nonsymmetric approximation in spaces of integrable functions. Zbl 0522.41028 Babenko, V. F. 6 1983 Inequalities for rearrangements of differentiable periodic functions, approximation problems, and approximate integration. Zbl 0547.41027 Babenko, V. F. 6 1983 Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions. Zbl 1224.41041 Babenko, V. F.; Parfinovych, N. V.; Pichugov, S. A. 6 2010 A property of compact operators in the space of integrable functions. Zbl 0492.47018 Babenko, V. F.; Pichugov, S. A. 6 1982 On the optimization of weighted quadrature formulas. Zbl 0885.41020 Babenko, V. F. 5 1995 On the relative widths of classes of functions with bounded mixed derivative. Zbl 0862.41019 Babenko, Vladislav F. 5 1996 Inequalities for the derivatives of polynomials with real zeros. Zbl 0641.42001 Babenko, V. F.; Pichugov, S. A. 5 1986 Faithful asymptotics of remainders optimal for some classes of functions with cubic weight formulas. Zbl 0359.41009 Babenko, V. F. 5 1977 Die Interpolation stetiger Abbildungen vermittels stückweise linearer. Zbl 0391.41001 Babenko, V. F. 5 1978 Über die Interpolation vermittels polyedrischer Funktionen. Zbl 0318.41024 Babenko, V. F.; Ligun, A. A. 5 1975 Bernstein-type inequalities for splines defined on the real axis. Zbl 1242.41011 Babenko, V. F.; Zontov, V. A. 5 2011 Approximation of some classes of set-valued periodic functions by generalized trigonometric polynomials. Zbl 1490.42003 Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V. 4 2016 Nonsymmetric approximation in the mean of differentiable functions by algebraic polynomials. Zbl 0677.41007 Babenko, V. F.; Kofanov, V. A. 4 1988 Über die beste lineare Approximation gewisser Klassen differenzierbarer periodischer Funktionen. Zbl 0444.41010 Babenko, V. F.; Pichugov, S. A. 4 1980 On exact inequalities of Hardy-Littlewood-Pólya type. Zbl 0956.46023 Babenko, Vladislav F.; Rassias, Themistocles M. 4 2000 On optimization of approximate integration over \(d\)-dimensional ball. Zbl 1111.41021 Babenko, V. F.; Borodachov, S. V. 4 2003 Die Ordnung der besten einseitigen Approximationen vermittels Polynome und Splinefunktionen in der \(L_p\)-Metrik. Zbl 0341.41016 Babenko, V. F.; Ligun, A. A. 4 1976 Optimal recovery of operators in function \(L\)-spaces. Zbl 1488.46070 Babenko, V.; Babenko, V.; Kovalenko, O.; Polishchuk, M. 4 2021 An exact inequality for the derivative of a trigonometric polynomial having only real zeros. Zbl 0616.42001 Babenko, V. F.; Pichugov, S. A. 4 1986 On asymptotical behavior of the optimal linear spline interpolation error of \(C^2\) functions. Zbl 1487.41008 Babenko, Vladislav; Babenko, Yuliya; Ligun, Anatoliy; Shumeiko, Alexander 4 2006 Kolmogorov type inequalities for fractional derivatives of Hölder functions of two variables. Zbl 1487.41012 Babenko, V.; Pichugov, S. 4 2007 Nonsymmetric extremal problems in approximation theory. Zbl 0568.41032 Babenko, V. F. 4 1983 Approximation of convolution classes. Zbl 0693.42001 Babenko, V. F. 4 1987 On best uniform approximation by splines in the presence of restrictions on their derivatives. Zbl 0798.41002 Babenko, V. F. 4 1991 Optimal recovery of convolutions and scalar products of functions from various classes. Zbl 0782.42010 Babenko, V. F.; Rudenko, A. A. 4 1991 On Jackson-type inequalities for functions defined on a sphere. Zbl 1103.41011 Babenko, V. F.; Doronin, V. G.; Ligun, A. A.; Shumeiko, A. A. 3 2005 On inequalities for norms of intermediate derivatives on a finite interval. Zbl 0887.26009 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 3 1995 On the optimal renewal of bilinear functionals in linear normed spaces. Zbl 0939.46016 Babenko, V. F.; Rudenko, A. A. 3 1997 Inequalities for norms of intermediate derivatives of periodic functions and their applications. Zbl 0920.26013 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 3 1997 Extremal problems in approximation theory, and inequalities for rearrangements. Zbl 0642.41019 Babenko, V. F. 3 1987 On the construction of optimal cubature formulae which use integrals over hyperspheres. Zbl 1114.41019 Babenko, V. F.; Borodachov, S. V. 3 2007 Kolmogorov inequalities for multiply monotone functions defined on a half-line. Zbl 1148.41011 Babenko, Vladislav; Babenko, Yuliya 3 2005 Optimal recovery of monotone operators in partially ordered \(L\)-spaces. Zbl 1448.41030 Babenko, Vladyslav; Babenko, Vira; Kovalenko, Oleg 3 2020 Optimization of approximate integration of set-valued functions monotone with respect to inclusion. Zbl 1245.49029 Babenko, V. F.; Babenko, V. V. 3 2011 Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line. Zbl 1336.26021 Babenko, Vladislav F.; Churilova, Mariya S.; Parfinovych, Nataliia V.; Skorokhodov, Dmytro S. 3 2014 Optimal recovery of integral operators and its applications. Zbl 1416.65563 Babenko, Vladyslav; Babenko, Yuliya; Parfinovych, Nataliia; Skorokhodov, Dmytro 3 2016 Approximation theory and harmonic analysis. (Теория аппроксимации и гармонический анализ.) Zbl 1349.42001 Motornyĭ, V. P.; Babenko, V. F.; Dovgosheĭ, A. A.; Kuznetsova, O. I. 3 2011 On the optimal recovery of integrals of set-valued functions. Zbl 1313.49022 Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V. 3 2014 On the optimal recovery of integrals of set-valued functions. Zbl 1386.41010 Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V. 3 2016 On the best use of linear functionals for the approximation of bilinear ones. Zbl 0511.41035 Babenko, V. F. 3 1979 Approximation of unbounded operators by bounded operators in a Hilbert space. Zbl 1221.47025 Babenko, V. F.; Bilichenko, R. O. 3 2009 Approximate computation of scalar products. Zbl 0712.42003 Babenko, V. F. 3 1988 Inequalities of Bernstein type for polynomial splines in \(L_ 2\). Zbl 0739.42002 Babenko, V. F.; Pichugov, S. A. 3 1991 On inequality of the type of Jackson’s inequalities for linear methods of function approximation. Zbl 0472.41011 Babenko, V. F.; Shalaev, V. V. 3 1980 Approximation in the mean of linear combinations of shifts of certain functions. Zbl 0499.41017 Babenko, V. F.; Pichugov, S. A. 3 1981 Exact values of best approximations for classes of periodic functions by splines of deficiency 2. Zbl 1204.41018 Babenko, V. F.; Parfinovich, N. V. 3 2009 The best \(L_ 1\)-approximations by splines in the presence of restrictions on their derivatives. Zbl 0848.42004 Babenko, V. F. 2 1992 On additive inequalities for intermediate derivatives of functions given on a finite interval. Zbl 0935.26004 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 2 1997 On Chebyshev rank in \(L_1\)-approximation. Zbl 0893.41017 Babenko, V. F.; Polyakov, O. V.; Tractinskaya, V. N. 2 1997 On Kolmogorov-type inequalities for functions defined on a semiaxis. Zbl 1164.41319 Babenko, V. F.; Skorokhodov, D. S. 2 2007 Exact Kolmogorov-type inequalities with bounded leading derivative in the case of low smoothness. Zbl 1008.41011 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 2 2001 Exact inequalities for norms of intermediate derivatives of half-integer order and their applications. Zbl 0929.41013 Babenko, V. F. 2 1997 On the Kolmogorov problem for the upper bounds of four consecutive derivatives of a multiply monotone function. Zbl 1125.26023 Babenko, Vladislav; Babenko, Yuliya 2 2007 On the best interval quadrature formulae for classes of differentiable periodic functions. Zbl 1147.41008 Babenko, V. F.; Skorokhodov, D. S. 2 2007 Sharp inequalities for the norms of conjugate functions and their applications. Zbl 0638.42012 Babenko, V. F. 2 1987 The best approximation of closed operators by bounded operators in Hilbert spaces. Zbl 1511.47015 Babenko, V. F.; Parfinovych, N. V.; Skorokhodov, D. S. 2 2022 On multivariate Ostrowski type inequalities and their applications. Zbl 1445.26017 Babenko, Vladyslav; Babenko, Yuliya; Kovalenko, Oleg 2 2020 Widths and best quadrature formulae for classes of convolutions. Zbl 0743.42001 Babenko, V. F. 2 1991 On Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces. Zbl 1495.47035 Babenko, V.; Babenko, Yu.; Kriachko, N.; Skorokhodov, D. 2 2021 Optimal cubature formulas related to tomography for certain classes of functions defined on a cube. Zbl 1262.41018 Babenko, Vladyslav; Borodachov, Sergiy; Skorokhodov, Dmytro 2 2011 Construction of optimal cubature formulas related to computer tomography. Zbl 1231.65054 Babenko, V. F.; Borodachov, S. V.; Skorokhodov, D. S. 2 2011 Inequalities of Taikov type for selfadjoint operators in Hilbert space. Zbl 1243.47042 Babenko, V. F.; Bilichenko, R. O. 2 2010 Exact asymptotics of the optimal \(L_p\)-error of asymmetric linear spline approximation. Zbl 1379.41006 Babenko, Vladislav; Babenko, Yuliya; Parfinovych, Nataliya; Skorokhodov, Dmytro 2 2014 On the exact values of the best approximations of classes of differentiable periodic functions by splines. Zbl 1290.41022 Babenko, V. F.; Parfinovich, N. V. 2 2010 Development of studies on the exact solution of extremal problems of the theory of best approximation. Zbl 0715.41038 Babenko, V. F.; Ligun, A. A. 2 1990 On the optimal piecewise linear interpolation of continuous mappings. Zbl 0473.41006 Babenko, V. F. 2 1980 Inequalities of the Kolmogorov type for norms of Riesz derivatives of multivariate functions and some of their applications. Zbl 1271.41004 Babenko, Vladislav F.; Parfinovich, Natal’ya V. 2 2012 Approximation of some classes of functions of many variables by harmonic splines. Zbl 1272.41006 Babenko, V. F.; Leskevich, T. Yu. 2 2013 Jackson-Stechkin-type inequalities for the approximation of elements of Hilbert spaces. Zbl 1428.41012 Babenko, V. F.; Konareva, S. V. 2 2019 Optimization of approximate integration of monotone functions of two variables. Zbl 0953.41020 Babenko, V. F.; Borodachev, S. V. 1 1999 On the optimal reconstruction of the convolution of \(n\) functions according to the linear information. Zbl 1498.42005 Babenko, V. F.; Gun’ko, M. S. 1 2016 Estimation of the uniform norm of one-dimensional Riesz potential of the partial derivative of a function with bounded Laplacian. Zbl 1499.42045 Babenko, V. F.; Parfinovich, N. V. 1 2016 Some extremal properties of polynomials and splines. Zbl 0813.41011 Babenko, V. F.; Ligun, A. A. 1 1991 On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net. Zbl 0941.46014 Babenko, V. F.; Vakarchuk, M. B. 1 1997 Inequalities for norms of intermediate derivatives and some of their applications. Zbl 0947.26015 Babenko, Vladislav F. 1 1998 Exact inequalities of Kolmogorov type for multivariate functions and their applications. Zbl 1054.41510 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 1997 Additive inequalities for intermediate derivatives of differentiable mappings of Banach spaces. Zbl 0927.46025 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 1998 On inequalities of Landau-Hadamard-Kolmogorov type for the \(L_ 2\)-norm of intermediate derivatives. Zbl 0868.46023 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 1996 On approximate computation of scalar products. Zbl 0656.42003 Babenko, V. F. 1 1988 The order of the best one-sided approximation by polynomials and splines in the \(L_p\)-metric. Zbl 0348.41019 Babenko, V. F.; Ligun, A. A. 1 1976 Interpolation of continuous maps by piecewise-linear maps. Zbl 0408.41002 Babenko, V. F. 1 1979 Estimates for wavelet coefficients on some classes of functions. Zbl 1164.42328 Babenko, V. F.; Spector, S. A. 1 2007 Fixed sets and fixed points for mappings in generalized \(\mathrm{Lim}\)-spaces of Fréchet. Zbl 1517.54013 Babenko, V. F.; Babenko, V. V.; Kovalenko, O. V. 1 2023 The best approximation of closed operators by bounded operators in Hilbert spaces. Zbl 1511.47015 Babenko, V. F.; Parfinovych, N. V.; Skorokhodov, D. S. 2 2022 On approximation of hypersingular integral operators by bounded ones. Zbl 1505.41002 Babenko, Vladyslav; Kovalenko, Oleg; Parfinovych, Nataliia 1 2022 Optimal recovery of operators in function \(L\)-spaces. Zbl 1488.46070 Babenko, V.; Babenko, V.; Kovalenko, O.; Polishchuk, M. 4 2021 On Hardy-Littlewood-Pólya and Taikov type inequalities for multiple operators in Hilbert spaces. Zbl 1495.47035 Babenko, V.; Babenko, Yu.; Kriachko, N.; Skorokhodov, D. 2 2021 On asymptotically optimal cubatures for multidimensional Sobolev spaces. Zbl 1502.41011 Babenko, V. F.; Babenko, Yu. V.; Kovalenko, O. V. 1 2021 Optimal recovery of monotone operators in partially ordered \(L\)-spaces. Zbl 1448.41030 Babenko, Vladyslav; Babenko, Vira; Kovalenko, Oleg 3 2020 On multivariate Ostrowski type inequalities and their applications. Zbl 1445.26017 Babenko, Vladyslav; Babenko, Yuliya; Kovalenko, Oleg 2 2020 Optimal recovery of elements of a Hilbert space and their scalar products according to the Fourier coefficients known with errors. Zbl 1455.65087 Babenko, V. F.; Gunko, M. S.; Parfinovych, N. V. 1 2020 Calculus and nonlinear integral equations for functions with values in \(L\)-spaces. Zbl 1449.45009 Babenko, V. 7 2019 Jackson-Stechkin-type inequalities for the approximation of elements of Hilbert spaces. Zbl 1428.41012 Babenko, V. F.; Konareva, S. V. 2 2019 Inequalities of Carlson-Taikov-Shadrin type in \(L_{2,r;\alpha,\beta}((-1,1))\) and \(L_{2,e^{-t^2}}(\mathbb{R})\) spaces. Zbl 1490.41006 Babenko, V. F.; Kozynenko, O. V.; Skorokhodov, D. S. 1 2019 Approximation of some classes of set-valued periodic functions by generalized trigonometric polynomials. Zbl 1490.42003 Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V. 4 2016 Optimal recovery of integral operators and its applications. Zbl 1416.65563 Babenko, Vladyslav; Babenko, Yuliya; Parfinovych, Nataliia; Skorokhodov, Dmytro 3 2016 On the optimal recovery of integrals of set-valued functions. Zbl 1386.41010 Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V. 3 2016 On the optimal reconstruction of the convolution of \(n\) functions according to the linear information. Zbl 1498.42005 Babenko, V. F.; Gun’ko, M. S. 1 2016 Estimation of the uniform norm of one-dimensional Riesz potential of the partial derivative of a function with bounded Laplacian. Zbl 1499.42045 Babenko, V. F.; Parfinovich, N. V. 1 2016 Inequalities of Hardy-Littlewood-Pólya type for functions of operators and their applications. Zbl 1350.26002 Babenko, Vladyslav; Babenko, Yuliya; Kriachko, Nadiia 1 2016 On modulus of continuity of differentiation operator on weighted Sobolev classes. Zbl 1391.26040 Babenko, Vladislav F.; Kovalenko, Oleg V. 1 2015 Kolmogorov’s problem on the class of multiply monotone functions. Zbl 1325.41007 Babenko, Vladyslav; Babenko, Yuliya; Kovalenko, Oleg 1 2015 Kolmogorov-type inequalities for norms of Riesz derivatives of functions of several variables with Laplacian bounded in \(L_\infty\) and related problems. Zbl 1314.41006 Babenko, V. F.; Parfinovich, N. V.; Pichugov, S. A. 8 2014 Kolmogorov type inequalities for the Marchaud fractional derivatives on the real line and the half-line. Zbl 1336.26021 Babenko, Vladislav F.; Churilova, Mariya S.; Parfinovych, Nataliia V.; Skorokhodov, Dmytro S. 3 2014 On the optimal recovery of integrals of set-valued functions. Zbl 1313.49022 Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V. 3 2014 Exact asymptotics of the optimal \(L_p\)-error of asymmetric linear spline approximation. Zbl 1379.41006 Babenko, Vladislav; Babenko, Yuliya; Parfinovych, Nataliya; Skorokhodov, Dmytro 2 2014 On interpolation and extremal properties of periodic perfect splines. Zbl 1324.41002 Babenko, V. F.; Kovalenko, O. V. 1 2014 Approximation of some classes of functions of many variables by harmonic splines. Zbl 1272.41006 Babenko, V. F.; Leskevich, T. Yu. 2 2013 Estimates of approximation of elements of Hilbert space. Zbl 1313.41019 Babenko, V. F.; Savela, S. V. 1 2013 Uniformly distributed ridge approximation of some classes of harmonic functions. Zbl 1276.42002 Babenko, V. F.; Levchenko, D. A. 1 2013 Kolmogorov type inequalities for norms of Riesz derivatives of multivariate functions and some applications. Zbl 1304.41008 Babenko, V. F.; Parfinovich, N. V. 7 2012 Inequalities of the Kolmogorov type for norms of Riesz derivatives of multivariate functions and some of their applications. Zbl 1271.41004 Babenko, Vladislav F.; Parfinovich, Natal’ya V. 2 2012 On the dependence of the norm of a function on the norms of its derivatives of orders \(k\), \(r-2\), and \(r\), \(0< k< r-2\). Zbl 1267.46043 Babenko, V. F.; Kovalenko, O. V. 1 2012 Bernstein-type inequalities for splines defined on the real axis. Zbl 1242.41011 Babenko, V. F.; Zontov, V. A. 5 2011 Optimization of approximate integration of set-valued functions monotone with respect to inclusion. Zbl 1245.49029 Babenko, V. F.; Babenko, V. V. 3 2011 Approximation theory and harmonic analysis. (Теория аппроксимации и гармонический анализ.) Zbl 1349.42001 Motornyĭ, V. P.; Babenko, V. F.; Dovgosheĭ, A. A.; Kuznetsova, O. I. 3 2011 Optimal cubature formulas related to tomography for certain classes of functions defined on a cube. Zbl 1262.41018 Babenko, Vladyslav; Borodachov, Sergiy; Skorokhodov, Dmytro 2 2011 Construction of optimal cubature formulas related to computer tomography. Zbl 1231.65054 Babenko, V. F.; Borodachov, S. V.; Skorokhodov, D. S. 2 2011 Sharp estimates of the norms of fractional derivatives of functions of several variables satisfying Hölder conditions. Zbl 1205.26008 Babenko, V. F.; Pichugov, S. A. 8 2010 Optimal recovery of isotropic classes of twice-differentiable multivariate functions. Zbl 1215.41001 Babenko, Vladislav F.; Borodachov, Sergiy V.; Skorokhodov, Dmytro S. 8 2010 Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions. Zbl 1224.41041 Babenko, V. F.; Parfinovych, N. V.; Pichugov, S. A. 6 2010 Inequalities of Taikov type for selfadjoint operators in Hilbert space. Zbl 1243.47042 Babenko, V. F.; Bilichenko, R. O. 2 2010 On the exact values of the best approximations of classes of differentiable periodic functions by splines. Zbl 1290.41022 Babenko, V. F.; Parfinovich, N. V. 2 2010 Approximation of unbounded operators by bounded operators in a Hilbert space. Zbl 1221.47025 Babenko, V. F.; Bilichenko, R. O. 3 2009 Exact values of best approximations for classes of periodic functions by splines of deficiency 2. Zbl 1204.41018 Babenko, V. F.; Parfinovich, N. V. 3 2009 Refinement of a Hardy-Littlewood-Pólya-type inequality for powers of self-adjoint operators in a Hilbert space. Zbl 1224.26068 Babenko, V. F.; Bilichenko, R. O. 1 2009 Exact asymptotics of the optimal \(L_{p,\Omega}\)-error of linear spline interpolation. Zbl 1217.41008 Babenko, Vladislav; Babenko, Yuliya; Skorokhodov, Dmytro 1 2008 On the best interval quadrature formulae for convolution classes. Zbl 1217.65055 Babenko, Vladislav; Skorokhodov, Dmytro 1 2008 Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic. Zbl 1131.26010 Babenko, Vladislav F.; Churilova, Mariya S. 6 2007 Kolmogorov type inequalities for fractional derivatives of Hölder functions of two variables. Zbl 1487.41012 Babenko, V.; Pichugov, S. 4 2007 On the construction of optimal cubature formulae which use integrals over hyperspheres. Zbl 1114.41019 Babenko, V. F.; Borodachov, S. V. 3 2007 On Kolmogorov-type inequalities for functions defined on a semiaxis. Zbl 1164.41319 Babenko, V. F.; Skorokhodov, D. S. 2 2007 On the Kolmogorov problem for the upper bounds of four consecutive derivatives of a multiply monotone function. Zbl 1125.26023 Babenko, Vladislav; Babenko, Yuliya 2 2007 On the best interval quadrature formulae for classes of differentiable periodic functions. Zbl 1147.41008 Babenko, V. F.; Skorokhodov, D. S. 2 2007 Estimates for wavelet coefficients on some classes of functions. Zbl 1164.42328 Babenko, V. F.; Spector, S. A. 1 2007 On asymptotical behavior of the optimal linear spline interpolation error of \(C^2\) functions. Zbl 1487.41008 Babenko, Vladislav; Babenko, Yuliya; Ligun, Anatoliy; Shumeiko, Alexander 4 2006 On Jackson-type inequalities for functions defined on a sphere. Zbl 1103.41011 Babenko, V. F.; Doronin, V. G.; Ligun, A. A.; Shumeiko, A. A. 3 2005 Kolmogorov inequalities for multiply monotone functions defined on a half-line. Zbl 1148.41011 Babenko, Vladislav; Babenko, Yuliya 3 2005 Kolmogorov-type inequalities and their applications. Zbl 1057.41006 Babenko, Vladislav 1 2004 The Kolmogorov inequality for absolutely monotone functions on a half-line. Zbl 1068.41021 Babenko, Vladislav; Babenko, Yuliya 1 2004 Approximation of sine-shaped functions by constants in spaces \(L_p,p<1\). Zbl 1089.41010 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 2004 On optimization of approximate integration of multivariate periodic functions. Zbl 1087.65531 Babenko, Vladislav F.; Borodachov, Sergiy V. 1 2004 Comparison of exact constants in inequalities for derivatives of functions defined on the real axis and a circle. Zbl 1103.26013 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 14 2003 On optimization of approximate integration over \(d\)-dimensional ball. Zbl 1111.41021 Babenko, V. F.; Borodachov, S. V. 4 2003 Comparison of rearrangement and Kolmogorov-Nagy type inequalities for periodic functions. Zbl 1034.41010 Babenko, Vladislav; Kofanov, Vladimir; Pichugov, Sergei 14 2002 On the Kolmogorov type inequalities for fractional derivatives. Zbl 1331.26028 Babenko, V. F.; Churilova, M. G. 8 2002 On Kolmogorov’s problem about existence of a function with given norms of its derivatives. Zbl 1145.41309 Babenko, V. F.; Britvin, Y. E. 1 2002 Exact Kolmogorov-type inequalities with bounded leading derivative in the case of low smoothness. Zbl 1008.41011 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 2 2001 The exact inequalities of the Kolmogorov type for functions of two variables. Zbl 1054.41503 Babenko, V. F. 6 2000 Investigations of Dnepropetrovsk mathematicians related to inequalities for derivatives of periodic functions and their applications. Zbl 0976.41001 Babenko, V. F. 6 2000 On exact inequalities of Hardy-Littlewood-Pólya type. Zbl 0956.46023 Babenko, Vladislav F.; Rassias, Themistocles M. 4 2000 On the uniqueness of an element of the best \(L_1\)-approximation for functions with values in a Banach space. Zbl 0978.41018 Babenko, V. F.; Gorbenko, M. E. 1 2000 Optimization of approximate integration of monotone functions of two variables. Zbl 0953.41020 Babenko, V. F.; Borodachev, S. V. 1 1999 Inequalities of Kolmogorov type and some of their applications in approximation theory. Zbl 0909.41008 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 10 1998 Inequalities for norms of intermediate derivatives and some of their applications. Zbl 0947.26015 Babenko, Vladislav F. 1 1998 Additive inequalities for intermediate derivatives of differentiable mappings of Banach spaces. Zbl 0927.46025 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 1998 On exact inequalities of the Kolmogorov type which take into account the number of changes of signs of derivatives. Zbl 0930.41013 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 1998 The best \(L_1\)-approximations of classes of functions defined by differential operators in terms of generalized splines from these classes. Zbl 0942.41004 Babenko, V. F.; Leis, Azar 1 1998 Multivariate inequalities of Kolmogorov type and their applications. Zbl 0911.46024 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 12 1997 On the optimal renewal of bilinear functionals in linear normed spaces. Zbl 0939.46016 Babenko, V. F.; Rudenko, A. A. 3 1997 Inequalities for norms of intermediate derivatives of periodic functions and their applications. Zbl 0920.26013 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 3 1997 On additive inequalities for intermediate derivatives of functions given on a finite interval. Zbl 0935.26004 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 2 1997 On Chebyshev rank in \(L_1\)-approximation. Zbl 0893.41017 Babenko, V. F.; Polyakov, O. V.; Tractinskaya, V. N. 2 1997 Exact inequalities for norms of intermediate derivatives of half-integer order and their applications. Zbl 0929.41013 Babenko, V. F. 2 1997 On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net. Zbl 0941.46014 Babenko, V. F.; Vakarchuk, M. B. 1 1997 Exact inequalities of Kolmogorov type for multivariate functions and their applications. Zbl 1054.41510 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 1997 Additive inequalities for the norms of intermediate derivatives. Zbl 0984.41008 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 1997 Extremal properties of polynomials and splines. Based on the Russian edition 1992. Zbl 0976.41008 Korneichuk, N. P.; Ligun, A. A.; Babenko, V. F. 47 1996 On the relative widths of classes of functions with bounded mixed derivative. Zbl 0862.41019 Babenko, Vladislav F. 5 1996 On inequalities of Landau-Hadamard-Kolmogorov type for the \(L_ 2\)-norm of intermediate derivatives. Zbl 0868.46023 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 1 1996 On the optimization of weighted quadrature formulas. Zbl 0885.41020 Babenko, V. F. 5 1995 On inequalities for norms of intermediate derivatives on a finite interval. Zbl 0887.26009 Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A. 3 1995 Approximation of continuous vector functions. Zbl 0943.41502 Babenko, V. F.; Pichugov, S. A. 1 1994 Extremal properties of polynomials and splines. (Ehkstremal’nye svojstva polinomov i splajnov.) Zbl 0853.41006 Kornejchuk, N. P.; Babenko, V. F.; Ligun, A. A. 7 1992 The best \(L_ 1\)-approximations by splines in the presence of restrictions on their derivatives. Zbl 0848.42004 Babenko, V. F. 2 1992 Best approximations of classes of functions defined by means of the modulus of continuity. Zbl 0782.42002 Babenko, V. F. 1 1992 On best uniform approximation by splines in the presence of restrictions on their derivatives. Zbl 0798.41002 Babenko, V. F. 4 1991 Optimal recovery of convolutions and scalar products of functions from various classes. Zbl 0782.42010 Babenko, V. F.; Rudenko, A. A. 4 1991 Inequalities of Bernstein type for polynomial splines in \(L_ 2\). Zbl 0739.42002 Babenko, V. F.; Pichugov, S. A. 3 1991 Widths and best quadrature formulae for classes of convolutions. Zbl 0743.42001 Babenko, V. F. 2 1991 Some extremal properties of polynomials and splines. Zbl 0813.41011 Babenko, V. F.; Ligun, A. A. 1 1991 Widths and best quadrature formulas for convolution classes. Zbl 0786.42002 Babenko, V. F. 1 1991 ...and 32 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 173 Authors 49 Babenko, Vladyslav Fedorovych 17 Parfinovych, Nataliia Viktorivna 15 Kofanov, V. A. 15 Skorokhodov, Dmytro S. 14 Kovalenko, Oleg V. 9 Arestov, Vitaliĭ Vladimirovich 9 Liu, Yongping 7 Babenko, Viktor V. 7 Borodachov, Sergiy V. 7 Deikalova, Marina Valer’evna 7 Pichugov, S. A. 6 Babenko, Yuliya 6 Vinogradov, Oleg Leonidovich 4 Ganzburg, Michael Iosifovich 4 Glazyrina, Polina Yu. 4 Lasuriya, Robert Andreevich 4 Selvan, A. Antony 3 Akopyan, Roman Razmikovich 3 Babenko, Vira 3 Davydov, Oleg V. 3 Dyn, Nira 3 Fang, Gensun 3 Farkhi, Elza M. 3 Gun’ko, M. S. 3 Li, Xuehua 3 Ligun, A. A. 3 Ling, Bo 3 Mokhov, Alona 3 Motornyĭ, Vitaliĭ Pavlovych 3 Révész, Szilárd György 3 Rudenko, A. A. 3 Serdyuk, Anatoly S. 3 Sommer, Manfred 3 Xiao, Weiwei 2 Berdysheva, Elena E. 2 Boyanov, Borislav Dechev 2 Chu, Yuming 2 Churilova, Mariya S. 2 Feki, Imed 2 Hayotov, Abdullo Rakhmonovich 2 Kriachko, Nadiia 2 Malykhin, Yuriĭ Vyacheslavovich 2 Naidenov, Nikola 2 Nfata, Houda 2 Novak, Erich 2 Novikov, Sergey I. 2 Polishchuk, M. V. 2 Polyakov, O. V. 2 Popovich, I. V. 2 Shadimetov, Kholmat Mahkambaevich 2 Sorokina, Tatyana 2 Tikhonov, Sergey Yur’evich 2 Yang, Lianhong 2 Zhao, Tiehong 2 Zhou, Songping 1 Abdullayev, Fahreddin G. 1 Abramovich, Yuriĭ Aleksandrovich 1 Ahmad, Bashir 1 Ainsworth, Mark 1 Akgun, Ramazan 1 Akopyan, O. V. 1 Alexandrova, T. V. 1 Aliprantis, Charalambos Dionisios 1 Al-saedi, Ahmed Eid Salem 1 Andreev, Andreĭ Stefanov 1 Babenko, Yu. V. 1 Boĭkov, Il’ya Vladimirovich 1 Bondarenko, A. R. 1 Burkinshaw, Owen 1 Bustamante González, Jorge 1 Cabada, Alberto 1 Chaĭchenko, Stanislav Olegovich 1 Cheney, Elliott Ward jun. 1 Evstigneev, Nikolai M. 1 Feschiev, Ivan Hristov 1 Flores-de-Jesús, Lázaro 1 Franchetti, Carlo 1 Gaidabura, A. E. 1 Gesztesy, Fritz 1 Ghosh, Riya 1 Gocheva-Ilieva, Snezhana Georgieva 1 Gruber, Peter Manfred 1 Gu, Yi 1 Horváth, Ágota P. 1 Hrabova, Ulyana Z. 1 Huang, Rong 1 Jørgensen, Palle E. T. 1 Kadets’, Volodymyr Mykhaĭlovych 1 Kholshevnikov, Konstantin Vladislavovich 1 Kirane, Mokhtar 1 Koç, Hüseyin 1 Kofanov, Volodymyr 1 Konareva, S. V. 1 Kovacs, Denis 1 Kozko, Artem Ivanovich 1 Kozynenko, O. V. 1 Kozynenko, Oleksandr 1 Kriachko, N. O. 1 Kumar, Anuj 1 Kuzmenko, Dmytro ...and 73 more Authors all top 5 Cited in 58 Serials 54 Ukrainian Mathematical Journal 22 Journal of Approximation Theory 20 Mathematical Notes 10 Analysis Mathematica 10 Proceedings of the Steklov Institute of Mathematics 9 Journal of Complexity 8 Journal of Mathematical Analysis and Applications 8 Researches in Mathematics 7 Journal of Mathematical Sciences (New York) 4 Numerical Functional Analysis and Optimization 4 Constructive Approximation 3 Journal of Computational and Applied Mathematics 3 Vestnik St. Petersburg University. Mathematics 3 Journal of Inequalities and Applications 3 Mathematical Inequalities & Applications 2 Advances in Mathematics 2 The Annals of Statistics 2 Applied Mathematics and Computation 2 BIT 2 Functional Analysis and its Applications 2 Journal of Functional Analysis 2 Mathematische Nachrichten 2 Numerische Mathematik 2 Siberian Mathematical Journal 2 Acta Applicandae Mathematicae 2 Russian Mathematics 2 St. Petersburg Mathematical Journal 2 The Journal of Fourier Analysis and Applications 2 Abstract and Applied Analysis 2 Carpathian Mathematical Publications 2 Ural Mathematical Journal 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Journal d’Analyse Mathématique 1 Czechoslovak Mathematical Journal 1 Cybernetics 1 Computer Aided Geometric Design 1 Aequationes Mathematicae 1 Cybernetics and Systems Analysis 1 Russian Journal of Mathematical Physics 1 Sbornik: Mathematics 1 Nonlinear Dynamics 1 Matematychni Studiï 1 Fractional Calculus & Applied Analysis 1 Revista Matemática Complutense 1 Acta Mathematica Sinica. English Series 1 Differential Equations 1 Computational Methods and Function Theory 1 Journal of Applied Mathematics and Computing 1 Hacettepe Journal of Mathematics and Statistics 1 Analysis and Applications (Singapore) 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Sibirskie Èlektronnye Matematicheskie Izvestiya 1 Complex Analysis and Operator Theory 1 Science China. Mathematics 1 Journal of Siberian Federal University. Mathematics & Physics 1 Constructive Mathematical Analysis all top 5 Cited in 27 Fields 159 Approximations and expansions (41-XX) 46 Harmonic analysis on Euclidean spaces (42-XX) 40 Real functions (26-XX) 35 Functional analysis (46-XX) 34 Numerical analysis (65-XX) 18 Operator theory (47-XX) 13 Functions of a complex variable (30-XX) 8 Ordinary differential equations (34-XX) 6 Convex and discrete geometry (52-XX) 5 Partial differential equations (35-XX) 5 Information and communication theory, circuits (94-XX) 3 Measure and integration (28-XX) 3 Special functions (33-XX) 3 General topology (54-XX) 3 Probability theory and stochastic processes (60-XX) 2 Potential theory (31-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Sequences, series, summability (40-XX) 2 Integral equations (45-XX) 2 Statistics (62-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Systems theory; control (93-XX) Citations by Year