Widths of classes from \(L_2[0,2\pi]\) and minimization of exact constants in Jackson-type inequalities

DOI10.1007/BF02675582zbMath0960.42002MaRDI QIDQ1974375

M. G. Esmaganbetov

Publication date: 1 May 2001

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

zbMATH Keywords

modulus of smoothnessKolmogorov width\(2\pi\)-periodic functionsexact constantslinear widthJackson-type inequalitiesprojection width

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (15)

Inequalities between best polynomial approximations and some smoothness characteristics in the space \(L_2\) and widths of classes of functions ⋮ On the best polynomial approximation in the space \(L_2\) and widths of some classes of functions ⋮ On widths of periodic functions in \(L_2\) ⋮ Jackson-type inequalities and widths of function classes in \(L_{2}\) ⋮ On estimates of diameter values of classes of functions in the weight space \(L_{2, \gamma } ( \mathbb{R}^2)\), \(\gamma = \exp(-x^2 - y^2)\) ⋮ Widths of certain classes of periodic functions in \(L_2\) ⋮ Best polynomial approximations in \(L_{2}\) of classes of \(2{\pi}\)-periodic functions and exact values of their widths ⋮ Unnamed Item ⋮ Jackson-type inequalities with generalized modulus of continuity and exact values of the \(n\)-widths for the classes of \((\psi,\beta)\)-differentiable functions in \(L_2\). III ⋮ 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 ⋮ Exact constants in Jackson-type inequalities and exact values of the widths of some classes of functions in \(L_{2}\) ⋮ Jackson-type inequalities and widths of functional classes in the Musielak-Orlicz type spaces ⋮ Widths of some functional classes in the space \(L_2\) on a period ⋮ Widths of functional classes defined by the majorants of generalized moduli of smoothness in the spaces \(\mathcal{S}^p\)

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