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Widths of functional classes defined by the majorants of generalized moduli of smoothness in the spaces \(\mathcal{S}^p\). (English. Ukrainian original) Zbl 1492.41009

Ukr. Math. J. 73, No. 6, 841-858 (2021); translation from Ukr. Mat. Zh. 73, No. 6, 723-737 (2021).
Summary: We obtain exact Jackson-type inequalities in terms of the best approximations and averaged values of the generalized moduli of smoothness in the spaces \(\mathcal{S}^p\). For classes of periodic functions defined by certain conditions imposed on the average values of the generalized moduli of smoothness, we determine the exact values of the Kolmogorov, Bernstein, linear, and projective widths in the spaces \(\mathcal{S}^p \).

MSC:

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
41A25 Rate of convergence, degree of approximation
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