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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 . III

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Ukrainian Mathematical Journal Aims and scope

In the classes L ψ β,2 of 2π -periodic (ψ, β) -differentiable functions for which L ψ β  ∈ L 2, we determine the exact constants in Jackson-type inequalities for the characteristic of smoothness \( {\varLambda}_{\upgamma}\left( f, t\right)={\left\{\frac{1}{t}{\displaystyle \underset{0}{\overset{t}{\int }}{\left\Vert {\varDelta}_h^{\upgamma}(f)\right\Vert}^2 d h}\right\}}^{1/2},\kern1em t>0, \), determined by averaging the norm of the generalized difference relation Δ γ h (f). For the classes of (ψ, β)-differentiable functions defined by using the characteristic of smoothness Λγ and the majorant Φ and satisfying numerous conditions, we establish the exact values of some n-widths in L2.

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  1. Nobel Dnepropetrovsk University, Dnepropetrovsk, Ukraine

    S. B. Vakarchuk

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 10, pp. 1299–1319, October, 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 . III. Ukr Math J 68, 1495–1518 (2017). https://doi.org/10.1007/s11253-017-1309-7

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  • DOI: https://doi.org/10.1007/s11253-017-1309-7

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