Jackson-type inequalities and widths of functional classes in the Musielak–Orlicz type spaces

Abstract

In the Musielak–Orlicz-type spaces ${\mathcal{𝒮}}_{\mathrm{M}}$, 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 ${\mathcal{𝒮}}_{\mathrm{M}}$ are found for classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness.