Widths of functional classes defined by majorants of generalized moduli of smoothness in the spaces ${\mathcal S}^{p}$
Abstract
UDC 517.5
We obtain exact Jackson-type inequalities in terms of best approximations and averaged values of generalized moduli of smoothness in spaces ${\mathcal S}^p$. For classes of periodic functions defined by certain conditions on the averaged values of the generalized moduli of smoothness, the Kolmogorov, Bernstein, linear, and projective widths in the spaces ${\mathcal S}^p$ are found.
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