Abstract
We obtain exact constants in Jackson-type inequalities for smoothness characteristics Λ k (f), k ∈ N, defined by averaging the kth-order finite differences of functions f ∈ L 2. On the basis of this, for differentiable functions in the classes L r2 , r ∈ N, we refine the constants in Jackson-type inequalities containing the kth-order modulus of continuity ω k . For classes of functions defined by their smoothness characteristics Λ k (f) and majorants Φ satisfying a number of conditions, we calculate the exact values of certain n-widths.
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Original Russian Text © S. B. Vakarchuk, V. I. Zabutnaya, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 2, pp. 215–238.
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Vakarchuk, S.B., Zabutnaya, V.I. Inequalities between best polynomial approximations and some smoothness characteristics in the space L 2 and widths of classes of functions. Math Notes 99, 222–242 (2016). https://doi.org/10.1134/S0001434616010259
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DOI: https://doi.org/10.1134/S0001434616010259