Shabozov M. Sh.
Exact Jackson - Stechkin-type inequalities for 2π -periodic functions in L 2 and widths of some classes of functions
Ukr. Mat. Zh. - 2011. - 63, № 10. - pp. 1434-1440
We consider the problem of finding exact inequalities for the best approximations of periodical differentiable functions by trigonometric polynomials and the m -order moduli of continuity in the space L 2 and present their applications. For some classes of functions defined by the indicated moduli of continuity, we calculate the exact values of n-widths in the space L 2 .
On exact values of quasiwidths for some classes of differentiable periodic functions of two variables
Ukr. Mat. Zh. - 2009. - 61, № 6. - pp. 855-864
We determine the exact values of Kolmogorov and linear quasiwidths for some classes of differentiable periodic functions of two variables in the Hilbert space $L_2(Q)$.
Ukr. Mat. Zh. - 1998. - 50, № 8. - pp. 1147–1151
We study the problem of renewal of a solution of the Dirichlet boundary-value problem for a biharmonic equation on the basis of the known information about the boundary function. The obtained estimates of renewal error are unimprovable in certain cases.
Quasiwidths and optimization of methods of mixed approximation of multidimensional singular integrals with kernels of hilbert type
Ukr. Mat. Zh. - 1996. - 48, № 6. - pp. 753-770
We consider the problem of application of mixed methods to the construction of algorithms, optimal in accuracy, for the calculation of multidimensional singular integrals with Hilbert-type kernels. We propose a method for the optimization of cubature formulas for singular integrals with Hilbert-type kernels based on the theory of quasiwidths.
Ukr. Mat. Zh. - 1996. - 48, № 3. - pp. 301-308
In the Hilbert space L 2(Δ2), Δ = [0, 2 π] we establish exact estimates of the Kolmogorov quasiwidths of some classes of periodic functions of two variables whose averaged modules of smoothness of mixed derivatives are majorizable by given functions.
Best approximation and best unilateral approximation of the kernel of a biharmonic equation and optimal renewal of the values of operators
Ukr. Mat. Zh. - 1995. - 47, № 11. - pp. 1549–1557
For the classB p ρ , 0 ≤ ρ < 1, 1≤p ≤ ∞, of 2π-periodic functions of the form f(t)=u(ρ,t), whereu (ρ,t) is a biharmonic function in the unit disk, we obtain the exact values of the best approximation and best unilateral approximation of the kernel Kρ(t) of the convolution f= Kρ *g, ∥g∥ρ≤l, with respect to the metric of L1. We also consider the problem of renewal of the values of the convolution operator by using the information about the values of the boundary functions.
An approach to the investigation of optimal quadrature formulas for singular integrals with fixed singularity
Ukr. Mat. Zh. - 1995. - 47, № 9. - pp. 1300–1304
For classes of functions given on the segment [0,1], we obtain optimal quadrature formulas for singular integrals with fixed singularity. The obtained results are extended to the case of two-dimensional integrals.
Ukr. Mat. Zh. - 1991. - 43, № 12. - pp. 1712–1716