We consider the generalized characteristics of smoothness of the functions ωw(f, t) and Λw(f, t), t > 0, in the space L2(ℝ) and on the classes \( {L}_2^{\alpha } \) (ℝ) defined with the help of fractional-order derivatives α ϵ (0, ∞) and obtain the exact Jackson-type inequalities for ωw(f).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 9, pp. 1166–1191, September, 2018.
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Vakarchuk, S.B. Generalized Characteristics of Smoothness and Some Extreme Problems of the Approximation Theory of Functions in the Space L2(ℝ). I. Ukr Math J 70, 1345–1374 (2019). https://doi.org/10.1007/s11253-019-01585-z
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DOI: https://doi.org/10.1007/s11253-019-01585-z