Estimates for functionals with a known, finite set of moments, in terms of moduli of continuity, and behavior of constants, in the Jackson-type inequalities

DOI10.1090/S1061-0022-2013-01261-1zbMath1275.41016MaRDI QIDQ2849196

V. V. Zhuk, O. L. Vinogradov

Publication date: 17 September 2013

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

modulus of continuitybest approximationsharp constantsJackson inequalitiesSteklov functions

Mathematics Subject Classification ID

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

Related Items (12)

On constants in estimates of approximations by entire functions of exponential type in terms of moduli of continuity of derivatives ⋮ Estimates for constant in Jackson type inequality for periodic functions ⋮ Improvement of Jackson type inequalities for moduli of continuity of order 4, 6, 8 ⋮ On Jackson type inequalities for the best approximations of periodic functions ⋮ Jackson type inequalities for deviations of the Riesz averages and applications to estimates of functionals with two known moments ⋮ Linear methods in the proof of Jackson type inequalities and applications to estimates of functionals with two known moments ⋮ Modified Steklov functions and numerical differentiation formulas ⋮ Estimates of moments of deviations of the Riesz averages and applications to Jackson type inequalities ⋮ Constants in Jackson type inequalities for the best approximation of periodic functions such that some of their Fourier coefficients vanish ⋮ On Rogosinski-type approximation processes in Banach space using the framework of the cosine operator function ⋮ On Window Methods in Generalized Shannon Sampling Operators ⋮ On constants in the generalized Jackson theorem

Cites Work

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• Estimates for functionals with a known moment sequence in terms of deviations of Steklov type means
• The rate of decrease of constants in Jackson type inequalities in dependence of the order of the continuity modulus
• Sharp inequalities for approximations of classes of periodic convolutions by odd-dimensional subspaces of shifts
• Sharp Kolmogorov-type inequalities for moduli of continuity and best approximations by trigonometric polynomials and splines
• Approximation of functions in the spaces \(L_ p\)
• On the exact constant in the Jackson-Stechkin inequality for the uniform metric

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