21 citations · 37 across the 13 of their papers we have counts for
13 papers
Direct and inverse theorems on the approximation of almost periodic functions in Besicovitch-Stepanets spaces
Anatolii Serdyuk, Andrii Shidlich
Direct and inverse approximation theorems are proved in the Besicovitch-Stepanets spaces of almost periodic functions in terms of the best approximations of fun…
Problems of approximation theory in abstract linear spaces
Anatolii S. Serdyuk, Andrii L. Shidlich
This review paper presents the results, which cover the study of current problems of approximation theory in abstract linear spaces. Such research has been actively developed since…
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…