Inequalities between best polynomial approximants and smoothness characteristics of functions in \(L_2\)

DOI10.1134/S000143462109011XzbMath1482.41007OpenAlexW3210120932MaRDI QIDQ2666611

Mirgand Shabozovich Shabozov

Publication date: 23 November 2021

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

Full work available at URL: https://doi.org/10.1134/s000143462109011x

zbMATH Keywords

upper boundfinite differencesbest approximationssmoothness characteristic

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Trigonometric polynomials, inequalities, extremal problems (42A05)

Related Items (1)

Estimate of the Hölder exponent based on the \(\epsilon\)-complexity of continuous functions

Cites Work

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• Inequalities between best polynomial approximations and some smoothness characteristics in the space \(L_2\) and widths of classes of functions
• Sharp Jackson-Stechkin type inequalities for periodic functions in \(L _{2}\) and widths of function classes
• On the best approximation of periodic functions by trigonometric polynomials and the exact values of widths of function classes in \(L_2\)
• 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-Stechkin type inequalities for special moduli of continuity and widths of function classes in the space \(L_2\)
• Problems in the approximation of \(2\pi \)-periodic functions by Fourier sums in the space \(L_2 (2\pi)\)
• Best polynomial approximations and the widths of function classes in \(L_2\)
• Estimates of the best approximations of periodic functions by trigonometric polynomials in terms of averaged differences and the multidimensional Jackson's theorem

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