arXiv subjects
Publications and source records attributed to A. L. Shidlich.
We calculated the exact value and found the polynomial of the best weighted polynomial approximation of the kernels of the form $\frac {A+Bx}{(x^2+λ^2)^2}$, where $A,B\in {\mathbb R}$, $λ>0$ in the mean-square metric.
In the Musielak-Orlicz type spaces ${\mathcal S}_{\bf M}$, exact Jackson-type inequalities are obtained in terms of best approximations of functions and the averaged values of their generalized moduli of smoothness. The values of Kolmogorov, Bernstein, linear, and projective widths in ${\mathcal S}_{\bf M}$ are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.