Abstract
Exact constants are found in inequalities of the Jackson–Stechkin type for smoothness characteristics \(\Lambda_{m}(f),\,m \in\mathbb{N}\) determined by averaging the norm in \(L_{2}\) of the mth order finite differences of the functions f. For classes of functions defined by the smoothness characteristic \(\Lambda_{m}(f)\), and the majorants \(\Phi\) satisfying a certain condition, the exact values of different n-widths are calculated.
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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 10, pp. 78–91.
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Shabozov, M.S., Abdulkhaminov, M.A. Some Inequalities Between the Best Polynomial Approximations and Averaged Finite-Difference Norms in Space L2. Russ Math. 65, 69–81 (2021). https://doi.org/10.3103/S1066369X21100078
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DOI: https://doi.org/10.3103/S1066369X21100078