Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in \(L_{2}\)

DOI10.1134/S0037446611060176zbMath1264.41015OpenAlexW2028224333MaRDI QIDQ662659

Mirgand Shabozovich Shabozov, Gulzorkhon Amirshoevich Yusupov

Publication date: 24 February 2012

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

Full work available at URL: https://doi.org/10.1134/s0037446611060176

zbMATH Keywords

widthbest approximationgeneralized continuity modulusextremal characteristicspace of square integrable functions

Mathematics Subject Classification ID

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

Related Items (12)

Generalized smoothness characteristics in Jackson-type inequalities and widths of classes of functions in \(L_2\) ⋮ Jackson-Stechkin Inequality and Values of Widths of Some Classes of Functions in $L_2$ ⋮ Inequalities between best polynomial approximations and some smoothness characteristics in the space \(L_2\) and widths of classes of functions ⋮ Exact constants in estimates of approximation of Lipschitz classes of periodic functions by Cesàro means ⋮ Jackson-type inequalities with generalized modulus of continuity and exact values of the \(n\)-widths for the classes of \((\psi,\beta)\)-differentiable functions in \(L_2\). I ⋮ Jackson-type inequalities and widths of functional classes in the Musielak-Orlicz type spaces ⋮ On the estimates of widths of the classes of functions defined by the generalized moduli of continuity and majorants in the weighted space \(L_{2,x}(0, 1)\) ⋮ Some inequalities between the best polynomial approximations and averaged finite-difference norms in space \(L_2\) ⋮ Sharp inequalities of Jackson-Stechkin type and widths of classes of functions in $L_{2}$ ⋮ Jackson-Stechkin-type inequalities for the approximation of elements of Hilbert spaces ⋮ On the value of the widths of some classes of functions from L_2 ⋮ 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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• Inequalities between the best approximations and homogenizations of moduli of continuity in the space \(L_{2}\)
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• The exact constant in the Jackson inequality in \(L^ 2\)
• Inequalities containing best approximations and the modulus of continuity of functions in \(L_2\)
• \(K\)-functionals and exact values of \(n\)-widths of some classes in \(L_2\)
• Widths of classes of periodic differentiable functions in the space \(L_{2} [0, 2\pi\)]
• Widths of classes from \(L_2[0,2\pi\) and minimization of exact constants in Jackson-type inequalities]
• The Jackson-Stechkin inequality in \(L^2\) with trigonometric modulus of continuity
• 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
• Best approximation of periodic functions by trigonometric polinomials in \(L_ 2\)
• DIRECT AND CONVERSE THEOREMS OF JACKSON TYPE IN $ L^p$ SPACES, $ 0<p<1$

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