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Asymptotic estimates for the best uniform approximations of classes of convolution of periodic functions of high smoothness
A. S. Serdyuk, I. V. Sokolenko
We find two-sides estimates for the best uniform approximations of classes of convolutions of -periodic functions from unit ball of the space with fixed…
Widths of functional classes defined by majorants of generalized moduli of smoothness in the spaces
Fahreddin Abdullayev, Anatolii Serdyuk, Andrii Shidlich
Exact Jackson-type inequalities are obtained in terms of best approximations and averaged values of generalized moduli of smoothness in the spaces . The values of K…
Approximation by interpolation trigonometric polynomials in metrics of the spaces on the classes of periodic entire functions
A. S. Serdyuk, I. V. Sokolenko
We obtain the asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with the equidistant nodes $x_k^{(n-1)}=\frac{2kπ}{2n-1}…
Approximation of classes of convolutions of periodic functions by linear methods constructed on basis of Fourier-Lagrange coefficients
A. S. Serdyuk, I. V. Sokolenko
We calculate the least upper bounds of pointwise and uniform approximations for classes of -periodic functions expressible as convolutions of an arbitrary square summable kerne…
Uniform approximations by Fourier sums on classes of generalized Poisson integrals
A. S. Serdyuk, T. A. Stepaniuk
We find asymptotic equalities for exact upper bounds of approximations by Fourier sums in uniform metric on classes of -periodic functions, representable in the form of convolu…
Asymptotic behavior of best approximations of classes of infinitely differentiable functions defined by moduli of continuity
A. S. Serdyuk, I. V. Sokolenko
We obtain asymptotic estimates for the best approximations by trigonometric polynomials in the metric space of classes of periodic functions that can be represented as…