Abstract
We consider and study properties of the smoothness characteristics \(\Omega _m (f,t)_{S^p } , m \in \mathbb{N}, t > 0\), of functions f(x) that belong to the space S p, 1 ≤ p < ∞, introduced by Stepanets. Exact inequalities of the Jackson type are obtained, and the exact values of the widths of the classes of functions defined by using Ωm(f,t)S p are calculated.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 3, pp. 303–316, March, 2006.
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Vakarchuk, S.B., Shchitov, A.N. On some extremal problems in the theory of approximation of functions in the spaces S p, 1 ≤ p < ∞. Ukr Math J 58, 340–356 (2006). https://doi.org/10.1007/s11253-006-0070-0
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DOI: https://doi.org/10.1007/s11253-006-0070-0