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Exact Jackson-type inequalities are obtained in terms of best approximationsand averaged values of generalized moduli of smoothness in the spaces${\mathcal S}^p$. The values of Kolmogorov, Bernstein, linear, and projectivewidths in the spaces ${\mathcal S}^p$ are found for classes of periodicfunctions defined by certain conditions on the averaged values of thegeneralized moduli of smoothness.

Widths of functional classes defined by majorants of generalized moduli of smoothness in the spaces ${\mathcal S}^p$