On the best polynomial approximation in the space \(L_2\) and widths of some classes of functions

DOI10.1007/s11253-013-0707-8zbMath1270.42006OpenAlexW1998986707MaRDI QIDQ352127

V. I. Zabutnaya, Sergei B. Vakarchuk

Publication date: 4 July 2013

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

Full work available at URL: https://doi.org/10.1007/s11253-013-0707-8

zbMATH Keywords

modulus of continuitySteklov operator

Mathematics Subject Classification ID

Trigonometric approximation (42A10)

Related Items (6)

Generalized smoothness characteristics in Jackson-type inequalities and widths of 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 ⋮ Widths of some classes of functions defined by the generalized moduli of continuity \(\omega_\gamma\) in the space \(L_2\) ⋮ 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 with generalized modulus of continuity and exact values of the \(n\)-widths for the classes of \((\psi, \beta)\)-differentiable functions in \(L_2\). II ⋮ Jackson-type inequalities for the special moduli of continuity on the entire real axis and the exact values of mean \(\nu\)-widths for the classes of functions in the space \(L_2(\mathbb R)\)

Cites Work

• 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
• On the application of a generalized translation operator in the approximation theory
• 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 \(L_2 (2\pi)\)
• Comparison theorems for a generalized modulus of continuity
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