# zbMATH — the first resource for mathematics

Compute Distance To:
 Documents Indexed: 199 Publications since 1975, including 3 Books
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#### Co-Authors

 43 single-authored 46 Pichugov, S. A. 33 Kofanov, V. A. 16 Ligun, A. A. 12 Skorokhodov, Dmytro S. 11 Babenko, Yuliya 11 Parfinovich, Natal’ya V. 9 Borodachov, Sergiy V. 8 Kovalenko, Oleg V. 6 Korneĭchuk, Nikolaĭ Pavlovich 5 Churilova, Mariya S. 5 Polyakov, O. V. 4 Babenko, Viktor V. 4 Motornyĭ, Vitaliĭ Pavlovich 4 Parfinovych, Nataliia Viktorivna 4 Rudenko, A. A. 3 Bilichenko, R. O. 3 Gun’ko, M. S. 3 Pichugov, Sergei 3 Polishchuk, M. V. 2 Babenko, Yu. V. 2 Glushko, V. N. 2 Gorbenko, M. E. 2 Levchenko, D. A. 2 Parfinovych, Nataliya 2 Shalaev, V. V. 1 Azar, Laith Emil 1 Babenko, Vira 1 Britvin, Y. E. 1 Churilova, M. G. 1 Doronin, V. G. 1 Dovgoshey, Oleksiy Alfredovich 1 Kofanov, Vladimir 1 Konareva, S. V. 1 Kozlo, G. V. 1 Kriachko, Nadiia 1 Kuznetsova, Ol’ga I. 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 Samoĭlenko, Anatoliĭ Mykhaĭlovych 1 Savela, S. V. 1 Selivanova, S. A. 1 Shumeiko, A. A. 1 Spector, S. A. 1 Tkachenko, M. E. 1 Tractinskaya, V. N. 1 Traktinskaya, V. N. 1 Uédraogo, Zh. B. 1 Vakarchuk, Mihail B. 1 Velikin, V. L. 1 Zhiganova, G. S. 1 Zontov, V. A.
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#### Serials

 42 Ukraïns’kyĭ Matematychnyĭ Zhurnal 31 Ukrainian Mathematical Journal 18 East Journal on Approximations 17 Mathematical Notes 9 Dopovidi Natsional’noï Akademiï Nauk Ukraïny. Matematyka, Pryrodoznavstvo, Tekhnichni Nauky 5 Analysis Mathematica 5 Matematicheskie Zametki 5 Journal of Complexity 4 Soviet Mathematics. Doklady 4 Dopovidi Akademiï Nauk Ukraïni 4 Doklady Mathematics 3 Proceedings of the Steklov Institute of Mathematics 2 Journal of Mathematical Analysis and Applications 2 Constructive Approximation 2 Modelirovanie v Mekhanike 2 Journal of Inequalities and Applications 2 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 2 Jaen Journal on Approximation 1 Doklady Akademii Nauk Ukrainskoĭ SSR, Seriya A 1 Advances in Mathematics 1 Numerical Functional Analysis and Optimization 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 Mathematical Inequalities & Applications 1 Trudy Instituta Prikladnoĭ Matematiki i Mekhaniki 1 Banach Journal of Mathematical Analysis
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#### Fields

 160 Approximations and expansions (41-XX) 48 Real functions (26-XX) 44 Harmonic analysis on Euclidean spaces (42-XX) 23 Functional analysis (46-XX) 12 Numerical analysis (65-XX) 7 Operator theory (47-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 History and biography (01-XX) 2 Partial differential equations (35-XX) 2 Integral equations (45-XX) 2 Convex and discrete geometry (52-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX)

#### Citations contained in zbMATH Open

105 Publications have been cited 329 times in 177 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.
1996
Approximations, widths and optimal quadrature formulae for classes of periodic functions with rearrangements invariant sets of derivatives. Zbl 0652.41008
Babenko, V. F.
1987
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.
2003
Multivariate inequalities of Kolmogorov type and their applications. Zbl 0911.46024
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1997
Asymptotically sharp bounds for the remainder for the best quadrature formulas for several classes of functions. Zbl 0333.41024
Babenko, V. F.
1976
Inequalities of Kolmogorov type and some of their applications in approximation theory. Zbl 0909.41008
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1998
Optimal recovery of isotropic classes of twice-differentiable multivariate functions. Zbl 1215.41001
Babenko, Vladislav F.; Borodachov, Sergiy V.; Skorokhodov, Dmytro S.
2010
On the optimal error bound for cubature formulae on certain classes of continuous functions. Zbl 0372.41020
Babenko, V. F.
1977
Comparison of rearrangement and Kolmogorov-Nagy type inequalities for periodic functions. Zbl 1034.41010
2002
Inequalities for rearrangements of differentiable periodic functions, approximation problems, and approximate integration. Zbl 0547.41027
Babenko, V. F.
1983
On the relative widths of classes of functions with bounded mixed derivative. Zbl 0862.41019
1996
A property of compact operators in the space of integrable functions. Zbl 0492.47018
Babenko, V. F.; Pichugov, S. A.
1982
The exact inequalities of the Kolmogorov type for functions of two variables. Zbl 1054.41503
Babenko, V. F.
2000
Investigations of Dnepropetrovsk mathematicians related to inequalities for derivatives of periodic functions and their applications. Zbl 0976.41001
Babenko, V. F.
2000
Über die Interpolation vermittels polyedrischer Funktionen. Zbl 0318.41024
Babenko, V. F.; Ligun, A. A.
1975
Die Interpolation stetiger Abbildungen vermittels stückweise linearer. Zbl 0391.41001
Babenko, V. F.
1978
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.
2010
On the Kolmogorov type inequalities for fractional derivatives. Zbl 1331.26028
Babenko, V. F.; Churilova, M. G.
2002
Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic. Zbl 1131.26010
Babenko, Vladislav F.; Churilova, Mariya S.
2007
Nonsymmetric approximation in spaces of integrable functions. Zbl 0522.41028
Babenko, V. F.
1983
On the optimization of weighted quadrature formulas. Zbl 0885.41020
Babenko, V. F.
1995
Die Ordnung der besten einseitigen Approximationen vermittels Polynome und Splinefunktionen in der $$L_p$$-Metrik. Zbl 0341.41016
Babenko, V. F.; Ligun, A. A.
1976
Faithful asymptotics of remainders optimal for some classes of functions with cubic weight formulas. Zbl 0359.41009
Babenko, V. F.
1977
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.
2014
Nonsymmetric approximation in the mean of differentiable functions by algebraic polynomials. Zbl 0677.41007
Babenko, V. F.; Kofanov, V. A.
1988
Sharp Kolmogorov-type inequalities for norms of fractional derivatives of multivariate functions. Zbl 1224.41041
Babenko, V. F.; Parfinovych, N. V.; Pichugov, S. A.
2010
Inequalities for the derivatives of polynomials with real zeros. Zbl 0641.42001
Babenko, V. F.; Pichugov, S. A.
1986
Bernstein-type inequalities for splines defined on the real axis. Zbl 1242.41011
Babenko, V. F.; Zontov, V. A.
2011
On inequality of the type of Jackson’s inequalities for linear methods of function approximation. Zbl 0472.41011
Babenko, V. F.; Shalaev, V. V.
1980
Approximation in the mean of linear combinations of shifts of certain functions. Zbl 0499.41017
Babenko, V. F.; Pichugov, S. A.
1981
Inequalities for norms of intermediate derivatives of periodic functions and their applications. Zbl 0920.26013
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1997
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.
2014
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.
2011
Approximation of convolution classes. Zbl 0693.42001
Babenko, V. F.
1987
Nonsymmetric extremal problems in approximation theory. Zbl 0568.41032
Babenko, V. F.
1983
An exact inequality for the derivative of a trigonometric polynomial having only real zeros. Zbl 0616.42001
Babenko, V. F.; Pichugov, S. A.
1986
Extremal problems in approximation theory, and inequalities for rearrangements. Zbl 0642.41019
Babenko, V. F.
1987
Exact values of best approximations for classes of periodic functions by splines of deficiency 2. Zbl 1204.41018
Babenko, V. F.; Parfinovich, N. V.
2009
Kolmogorov inequalities for multiply monotone functions defined on a half-line. Zbl 1148.41011
2005
On optimization of approximate integration over $$d$$-dimensional ball. Zbl 1111.41021
Babenko, V. F.; Borodachov, S. V.
2003
On the construction of optimal cubature formulae which use integrals over hyperspheres. Zbl 1114.41019
Babenko, V. F.; Borodachov, S. V.
2007
Optimization of approximate integration of set-valued functions monotone with respect to inclusion. Zbl 1245.49029
Babenko, V. F.; Babenko, V. V.
2011
Kolmogorov type inequalities for norms of Riesz derivatives of multivariate functions and some applications. Zbl 1304.41008
Babenko, V. F.; Parfinovich, N. V.
2012
Calculus and nonlinear integral equations for functions with values in $$L$$-spaces. Zbl 1449.45009
Babenko, V.
2019
On the Kolmogorov problem for the upper bounds of four consecutive derivatives of a multiply monotone function. Zbl 1125.26023
2007
Über die beste lineare Approximation gewisser Klassen differenzierbarer periodischer Funktionen. Zbl 0444.41010
Babenko, V. F.; Pichugov, S. A.
1980
On Chebyshev rank in $$L_1$$-approximation. Zbl 0893.41017
Babenko, V. F.; Polyakov, O. V.; Tractinskaya, V. N.
1997
On the optimal renewal of bilinear functionals in linear normed spaces. Zbl 0939.46016
Babenko, V. F.; Rudenko, A. A.
1997
On inequalities for norms of intermediate derivatives on a finite interval. Zbl 0887.26009
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1995
The best $$L_ 1$$-approximations by splines in the presence of restrictions on their derivatives. Zbl 0848.42004
Babenko, V. F.
1992
Exact inequalities for norms of intermediate derivatives of half-integer order and their applications. Zbl 0929.41013
Babenko, V. F.
1997
On exact inequalities of Hardy-Littlewood-Pólya type. Zbl 0956.46023
Babenko, Vladislav F.; Rassias, Themistocles M.
2000
Exact asymptotics of the optimal $$L_p$$-error of asymmetric linear spline approximation. Zbl 1379.41006
Babenko, Vladislav; Babenko, Yuliya; Parfinovych, Nataliya; Skorokhodov, Dmytro
2014
On the optimal recovery of integrals of set-valued functions. Zbl 1313.49022
Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V.
2014
Inequalities of Bernstein type for polynomial splines in $$L_ 2$$. Zbl 0739.42002
Babenko, V. F.; Pichugov, S. A.
1991
On best uniform approximation by splines in the presence of restrictions on their derivatives. Zbl 0798.41002
Babenko, V. F.
1991
Optimal recovery of convolutions and scalar products of functions from various classes. Zbl 0782.42010
Babenko, V. F.; Rudenko, A. A.
1991
Approximate computation of scalar products. Zbl 0712.42003
Babenko, V. F.
1988
Approximation of unbounded operators by bounded operators in a Hilbert space. Zbl 1221.47025
Babenko, V. F.; Bilichenko, R. O.
2009
Widths and best quadrature formulae for classes of convolutions. Zbl 0743.42001
Babenko, V. F.
1991
Sharp inequalities for the norms of conjugate functions and their applications. Zbl 0638.42012
Babenko, V. F.
1987
Optimal cubature formulas related to tomography for certain classes of functions defined on a cube. Zbl 1262.41018
Babenko, Vladyslav; Borodachov, Sergiy; Skorokhodov, Dmytro
2011
On the best interval quadrature formulae for classes of differentiable periodic functions. Zbl 1147.41008
Babenko, V. F.; Skorokhodov, D. S.
2007
On Kolmogorov-type inequalities for functions defined on a semiaxis. Zbl 1164.41319
Babenko, V. F.; Skorokhodov, D. S.
2007
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.
2005
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.
2010
Construction of optimal cubature formulas related to computer tomography. Zbl 1231.65054
Babenko, V. F.; Borodachov, S. V.; Skorokhodov, D. S.
2011
Optimization of approximate integration of monotone functions of two variables. Zbl 0953.41020
Babenko, V. F.; Borodachev, S. V.
1999
On the optimal piecewise linear interpolation of continuous mappings. Zbl 0473.41006
Babenko, V. F.
1980
On the best use of linear functionals for the approximation of bilinear ones. Zbl 0511.41035
Babenko, V. F.
1979
Exact inequalities of Kolmogorov type for multivariate functions and their applications. Zbl 1054.41510
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1997
Additive inequalities for intermediate derivatives of differentiable mappings of Banach spaces. Zbl 0927.46025
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1998
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.
2001
Additive inequalities for the norms of intermediate derivatives. Zbl 0984.41008
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1997
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.
2000
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
1998
Approximation of continuous vector functions. Zbl 0943.41502
Babenko, V. F.; Pichugov, S. A.
1994
Interpolation by polyhedral functions. Zbl 0327.41033
Babenko, V. F.; Ligun, A. A.
1976
Interpolation of continuous maps by piecewise-linear maps. Zbl 0408.41002
Babenko, V. F.
1979
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.
2004
On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net. Zbl 0941.46014
Babenko, V. F.; Vakarchuk, M. B.
1997
On the optimal recovery of integrals of set-valued functions. Zbl 1386.41010
Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V.
2016
Some extremal properties of polynomials and splines. Zbl 0813.41011
Babenko, V. F.; Ligun, A. A.
1991
Optimal recovery of integral operators and its applications. Zbl 1416.65563
Babenko, Vladyslav; Babenko, Yuliya; Parfinovych, Nataliia; Skorokhodov, Dmytro
2016
Widths and best quadrature formulas for convolution classes. Zbl 0786.42002
Babenko, V. F.
1991
Best approximations of classes of functions defined by means of the modulus of continuity. Zbl 0782.42002
Babenko, V. F.
1992
On approximate computation of scalar products. Zbl 0656.42003
Babenko, V. F.
1988
Exact asymptotics of the optimal $$L_{p,\Omega}$$-error of linear spline interpolation. Zbl 1217.41008
Babenko, Vladislav; Babenko, Yuliya; Skorokhodov, Dmytro
2008
On the best interval quadrature formulae for convolution classes. Zbl 1217.65055
2008
Comparison theorems and inequalities of Bernstein type. Zbl 0702.42001
Babenko, V. F.
1987
Nonsymetric approximations and inequalities for rearrangements in extremal problems of approximation theory. Zbl 0709.41505
Babenko, V. F.
1989
Approximations in the mean in the presence of constraints upon the derivatives of approximating functions. Zbl 0725.41021
Babenko, V. F.
1989
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.
2009
On optimization of approximate integration of multivariate periodic functions. Zbl 1087.65531
Babenko, Vladislav F.; Borodachov, Sergiy V.
2004
Kolmogorov-type inequalities and their applications. Zbl 1057.41006
2004
The Kolmogorov inequality for absolutely monotone functions on a half-line. Zbl 1068.41021
2004
Polynomials of fixed sign that deviate least from zero in the spaces $$L_ p$$. Zbl 0581.41009
Babenko, V. F.; Kofanov, V. A.
1985
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.
2012
On Kolmogorov’s problem about existence of a function with given norms of its derivatives. Zbl 1145.41309
Babenko, V. F.; Britvin, Y. E.
2002
Estimates for wavelet coefficients on some classes of functions. Zbl 1164.42328
Babenko, V. F.; Spector, S. A.
2007
Calculus and nonlinear integral equations for functions with values in $$L$$-spaces. Zbl 1449.45009
Babenko, V.
2019
On the optimal recovery of integrals of set-valued functions. Zbl 1386.41010
Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V.
2016
Optimal recovery of integral operators and its applications. Zbl 1416.65563
Babenko, Vladyslav; Babenko, Yuliya; Parfinovych, Nataliia; Skorokhodov, Dmytro
2016
Kolmogorov’s problem on the class of multiply monotone functions. Zbl 1325.41007
Babenko, Vladyslav; Babenko, Yuliya; Kovalenko, Oleg
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.
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.
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
2014
On the optimal recovery of integrals of set-valued functions. Zbl 1313.49022
Babenko, V. F.; Babenko, V. V.; Polishchuk, M. V.
2014
On interpolation and extremal properties of periodic perfect splines. Zbl 1324.41002
Babenko, V. F.; Kovalenko, O. V.
2014
Approximation of some classes of functions of many variables by harmonic splines. Zbl 1272.41006
Babenko, V. F.; Leskevich, T. Yu.
2013
Uniformly distributed ridge approximation of some classes of harmonic functions. Zbl 1276.42002
Babenko, V. F.; Levchenko, D. A.
2013
Estimates of approximation of elements of Hilbert space. Zbl 1313.41019
Babenko, V. F.; Savela, S. V.
2013
Kolmogorov type inequalities for norms of Riesz derivatives of multivariate functions and some applications. Zbl 1304.41008
Babenko, V. F.; Parfinovich, N. V.
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.
2012
Bernstein-type inequalities for splines defined on the real axis. Zbl 1242.41011
Babenko, V. F.; Zontov, V. A.
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.
2011
Optimization of approximate integration of set-valued functions monotone with respect to inclusion. Zbl 1245.49029
Babenko, V. F.; Babenko, V. V.
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
2011
Construction of optimal cubature formulas related to computer tomography. Zbl 1231.65054
Babenko, V. F.; Borodachov, S. V.; Skorokhodov, D. S.
2011
Optimal recovery of isotropic classes of twice-differentiable multivariate functions. Zbl 1215.41001
Babenko, Vladislav F.; Borodachov, Sergiy V.; Skorokhodov, Dmytro S.
2010
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.
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.
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.
2010
Exact values of best approximations for classes of periodic functions by splines of deficiency 2. Zbl 1204.41018
Babenko, V. F.; Parfinovich, N. V.
2009
Approximation of unbounded operators by bounded operators in a Hilbert space. Zbl 1221.47025
Babenko, V. F.; Bilichenko, R. O.
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.
2009
Exact asymptotics of the optimal $$L_{p,\Omega}$$-error of linear spline interpolation. Zbl 1217.41008
Babenko, Vladislav; Babenko, Yuliya; Skorokhodov, Dmytro
2008
On the best interval quadrature formulae for convolution classes. Zbl 1217.65055
2008
Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic. Zbl 1131.26010
Babenko, Vladislav F.; Churilova, Mariya S.
2007
On the construction of optimal cubature formulae which use integrals over hyperspheres. Zbl 1114.41019
Babenko, V. F.; Borodachov, S. V.
2007
On the Kolmogorov problem for the upper bounds of four consecutive derivatives of a multiply monotone function. Zbl 1125.26023
2007
On the best interval quadrature formulae for classes of differentiable periodic functions. Zbl 1147.41008
Babenko, V. F.; Skorokhodov, D. S.
2007
On Kolmogorov-type inequalities for functions defined on a semiaxis. Zbl 1164.41319
Babenko, V. F.; Skorokhodov, D. S.
2007
Estimates for wavelet coefficients on some classes of functions. Zbl 1164.42328
Babenko, V. F.; Spector, S. A.
2007
Kolmogorov inequalities for multiply monotone functions defined on a half-line. Zbl 1148.41011
2005
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.
2005
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.
2004
On optimization of approximate integration of multivariate periodic functions. Zbl 1087.65531
Babenko, Vladislav F.; Borodachov, Sergiy V.
2004
Kolmogorov-type inequalities and their applications. Zbl 1057.41006
2004
The Kolmogorov inequality for absolutely monotone functions on a half-line. Zbl 1068.41021
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.
2003
On optimization of approximate integration over $$d$$-dimensional ball. Zbl 1111.41021
Babenko, V. F.; Borodachov, S. V.
2003
Comparison of rearrangement and Kolmogorov-Nagy type inequalities for periodic functions. Zbl 1034.41010
2002
On the Kolmogorov type inequalities for fractional derivatives. Zbl 1331.26028
Babenko, V. F.; Churilova, M. G.
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.
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.
2001
The exact inequalities of the Kolmogorov type for functions of two variables. Zbl 1054.41503
Babenko, V. F.
2000
Investigations of Dnepropetrovsk mathematicians related to inequalities for derivatives of periodic functions and their applications. Zbl 0976.41001
Babenko, V. F.
2000
On exact inequalities of Hardy-Littlewood-Pólya type. Zbl 0956.46023
Babenko, Vladislav F.; Rassias, Themistocles M.
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.
2000
Optimization of approximate integration of monotone functions of two variables. Zbl 0953.41020
Babenko, V. F.; Borodachev, S. V.
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.
1998
Additive inequalities for intermediate derivatives of differentiable mappings of Banach spaces. Zbl 0927.46025
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
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
1998
Multivariate inequalities of Kolmogorov type and their applications. Zbl 0911.46024
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
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.
1997
On Chebyshev rank in $$L_1$$-approximation. Zbl 0893.41017
Babenko, V. F.; Polyakov, O. V.; Tractinskaya, V. N.
1997
On the optimal renewal of bilinear functionals in linear normed spaces. Zbl 0939.46016
Babenko, V. F.; Rudenko, A. A.
1997
Exact inequalities for norms of intermediate derivatives of half-integer order and their applications. Zbl 0929.41013
Babenko, V. F.
1997
Exact inequalities of Kolmogorov type for multivariate functions and their applications. Zbl 1054.41510
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1997
Additive inequalities for the norms of intermediate derivatives. Zbl 0984.41008
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1997
On inequalities of Kolmogorov-Hörmander type for functions bounded on a discrete net. Zbl 0941.46014
Babenko, V. F.; Vakarchuk, M. B.
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.
1996
On the relative widths of classes of functions with bounded mixed derivative. Zbl 0862.41019
1996
On the optimization of weighted quadrature formulas. Zbl 0885.41020
Babenko, V. F.
1995
On inequalities for norms of intermediate derivatives on a finite interval. Zbl 0887.26009
Babenko, V. F.; Kofanov, V. A.; Pichugov, S. A.
1995
Approximation of continuous vector functions. Zbl 0943.41502
Babenko, V. F.; Pichugov, S. A.
1994
The best $$L_ 1$$-approximations by splines in the presence of restrictions on their derivatives. Zbl 0848.42004
Babenko, V. F.
1992
Best approximations of classes of functions defined by means of the modulus of continuity. Zbl 0782.42002
Babenko, V. F.
1992
Inequalities of Bernstein type for polynomial splines in $$L_ 2$$. Zbl 0739.42002
Babenko, V. F.; Pichugov, S. A.
1991
On best uniform approximation by splines in the presence of restrictions on their derivatives. Zbl 0798.41002
Babenko, V. F.
1991
Optimal recovery of convolutions and scalar products of functions from various classes. Zbl 0782.42010
Babenko, V. F.; Rudenko, A. A.
1991
Widths and best quadrature formulae for classes of convolutions. Zbl 0743.42001
Babenko, V. F.
1991
Some extremal properties of polynomials and splines. Zbl 0813.41011
Babenko, V. F.; Ligun, A. A.
1991
Widths and best quadrature formulas for convolution classes. Zbl 0786.42002
Babenko, V. F.
1991
Nonsymetric approximations and inequalities for rearrangements in extremal problems of approximation theory. Zbl 0709.41505
Babenko, V. F.
1989
Approximations in the mean in the presence of constraints upon the derivatives of approximating functions. Zbl 0725.41021
Babenko, V. F.
1989
Nonsymmetric approximation in the mean of differentiable functions by algebraic polynomials. Zbl 0677.41007
Babenko, V. F.; Kofanov, V. A.
1988
Approximate computation of scalar products. Zbl 0712.42003
Babenko, V. F.
1988
On approximate computation of scalar products. Zbl 0656.42003
Babenko, V. F.
1988
Approximations, widths and optimal quadrature formulae for classes of periodic functions with rearrangements invariant sets of derivatives. Zbl 0652.41008
Babenko, V. F.
1987
Approximation of convolution classes. Zbl 0693.42001
Babenko, V. F.
1987
Extremal problems in approximation theory, and inequalities for rearrangements. Zbl 0642.41019
Babenko, V. F.
1987
Sharp inequalities for the norms of conjugate functions and their applications. Zbl 0638.42012
Babenko, V. F.
1987
Comparison theorems and inequalities of Bernstein type. Zbl 0702.42001
Babenko, V. F.
1987
Inequalities for the derivatives of polynomials with real zeros. Zbl 0641.42001
Babenko, V. F.; Pichugov, S. A.
1986
An exact inequality for the derivative of a trigonometric polynomial having only real zeros. Zbl 0616.42001
Babenko, V. F.; Pichugov, S. A.
1986
Polynomials of fixed sign that deviate least from zero in the spaces $$L_ p$$. Zbl 0581.41009
Babenko, V. F.; Kofanov, V. A.
1985
Inequalities for rearrangements of differentiable periodic functions, approximation problems, and approximate integration. Zbl 0547.41027
Babenko, V. F.
1983
Nonsymmetric approximation in spaces of integrable functions. Zbl 0522.41028
Babenko, V. F.
1983
Nonsymmetric extremal problems in approximation theory. Zbl 0568.41032
Babenko, V. F.
1983
A property of compact operators in the space of integrable functions. Zbl 0492.47018
Babenko, V. F.; Pichugov, S. A.
1982
Approximation in the mean of linear combinations of shifts of certain functions. Zbl 0499.41017
Babenko, V. F.; Pichugov, S. A.
1981
On inequality of the type of Jackson’s inequalities for linear methods of function approximation. Zbl 0472.41011
Babenko, V. F.; Shalaev, V. V.
1980
Über die beste lineare Approximation gewisser Klassen differenzierbarer periodischer Funktionen. Zbl 0444.41010
Babenko, V. F.; Pichugov, S. A.
1980
On the optimal piecewise linear interpolation of continuous mappings. Zbl 0473.41006
Babenko, V. F.
1980
On the best use of linear functionals for the approximation of bilinear ones. Zbl 0511.41035
Babenko, V. F.
1979
Interpolation of continuous maps by piecewise-linear maps. Zbl 0408.41002
Babenko, V. F.
1979
Die Interpolation stetiger Abbildungen vermittels stückweise linearer. Zbl 0391.41001
Babenko, V. F.
1978
On the optimal error bound for cubature formulae on certain classes of continuous functions. Zbl 0372.41020
Babenko, V. F.
1977
...and 5 more Documents
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#### Cited in 48 Serials

 48 Ukrainian Mathematical Journal 19 Journal of Approximation Theory 18 Mathematical Notes 9 Journal of Complexity 6 Journal of Mathematical Analysis and Applications 5 Analysis Mathematica 5 Journal of Mathematical Sciences (New York) 5 Proceedings of the Steklov Institute of Mathematics 3 Constructive Approximation 3 Vestnik St. Petersburg University. Mathematics 3 Journal of Inequalities and Applications 2 Advances in Mathematics 2 The Annals of Statistics 2 BIT 2 Functional Analysis and its Applications 2 Journal of Computational and Applied Mathematics 2 Journal of Functional Analysis 2 Numerical Functional Analysis and Optimization 2 Numerische Mathematik 2 Siberian Mathematical Journal 2 Russian Mathematics 2 St. Petersburg Mathematical Journal 2 The Journal of Fourier Analysis and Applications 2 Abstract and Applied Analysis 2 Mathematical Inequalities & Applications 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 Journal d’Analyse Mathématique 1 Applied Mathematics and Computation 1 Czechoslovak Mathematical Journal 1 Mathematische Nachrichten 1 Cybernetics 1 Acta Applicandae Mathematicae 1 Aequationes Mathematicae 1 Cybernetics and Systems Analysis 1 Russian Journal of Mathematical Physics 1 Nonlinear Dynamics 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 Analysis and Applications (Singapore) 1 International Journal of Wavelets, Multiresolution and Information Processing 1 Science China. Mathematics 1 Ural Mathematical Journal
all top 5

#### Cited in 29 Fields

 121 Approximations and expansions (41-XX) 32 Numerical analysis (65-XX) 29 Harmonic analysis on Euclidean spaces (42-XX) 27 Real functions (26-XX) 21 Functional analysis (46-XX) 12 Functions of a complex variable (30-XX) 10 Operator theory (47-XX) 6 Ordinary differential equations (34-XX) 6 Convex and discrete geometry (52-XX) 5 Partial differential equations (35-XX) 3 Special functions (33-XX) 3 Information and communication theory, circuits (94-XX) 2 Measure and integration (28-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral equations (45-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Systems theory; control (93-XX)