Inequalities between best polynomial approximations and some smoothness characteristics in the space \(L_2\) and widths of classes of functions

DOI10.1134/S0001434616010259zbMath1342.41033MaRDI QIDQ295993

V. I. Zabutnaya, Sergei B. Vakarchuk

Publication date: 14 June 2016

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

modulus of continuitybest polynomial approximationJackson-type inequalityRolle's theoremBernstein \(n\)-width of a function classsmoothness characteristics

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (8)

Exact constants in Jackson-type inequalities for the best mean square approximation in \(L_2(\mathbb{R})\) and exact values of mean \(\nu\)-widths of the classes of functions ⋮ Inequalities between best polynomial approximants and smoothness characteristics of functions in \(L_2\) ⋮ Widths of some classes of functions defined by the generalized moduli of continuity \(\omega_\gamma\) in the space \(L_2\) ⋮ Sharp inequalities between the best root-mean-square approximations of analytic functions in the disk and some smoothness characteristics in the Bergman space ⋮ Some inequalities between the best polynomial approximations and averaged finite-difference norms in space \(L_2\) ⋮ On the value of the widths of some classes of functions from L_2 ⋮ Direct and inverse approximation theorems in the Besicovitch-Musielak-Orlicz spaces of almost periodic functions ⋮ Exact inequalities between the best polynomial approximations and averaged norms of finite differences in the \(B_2\) space and widths of some classes of functions

Cites Work

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• On the best polynomial approximation in the space \(L_2\) and widths of some classes of functions
• Sharp Jackson-Stechkin type inequalities for periodic functions in \(L _{2}\) and widths of function classes
• Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in \(L_{2}\)
• Widths in \(L_ 2\) of classes of differentiable functions, defined by higher-order moduli of continuity
• A sharp inequality of Jackson-Stechkin type in \(L_{2}\) and the widths of functional classes
• Some inequalities between best approximations and moduli of continuity in an \(L_ 2 \)space
• Jackson-Stechkin type inequalities for special moduli of continuity and widths of function classes in the space \(L_2\)
• Widths of classes from \(L_2[0,2\pi\) and minimization of exact constants in Jackson-type inequalities]
• Problems in the approximation of \(2\pi \)-periodic functions by Fourier sums in the space \(L_2 (2\pi)\)
• Exact constants in Jackson-type inequalities and exact values of widths
• Estimates of the best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the multidimensional Jackson's theorem
• On Jackson's inequality for a generalized modulus of continuity in $ L_2$

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