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Jackson Theorem and Modulus of Continuity

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For the generalized moduli of continuity, including both the ordinary moduli of continuity and various their modifications, we establish the exact constants for Jackson-type inequalities on the classes of 2π -periodic functions in the space L 2 with (ψ, β) -derivatives introduced by Stepanets. These results take into account the classification of (ψ, β) -derivatives and enable us to consider the major part of Jackson-type inequalities obtained earlier in the classes of differentiable functions L r 2 , r ∈ ℕ, from the common point of view.

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Authors and Affiliations

  1. Nobel Dnepropetrovsk University, Dnepropetrovsk, Ukraine

    S. B. Vakarchuk

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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 68, No. 6, pp. 723–745, June, 2016.

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Vakarchuk, S.B. Jackson-Type Inequalities with Generalized Modulus of Continuity and Exact Values of the n-Widths for the Classes of (ψ, β)-Differentiable Functions in L 2. I. Ukr Math J 68, 823–848 (2016). https://doi.org/10.1007/s11253-016-1260-z

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