A direct theorem of approximation theory for a general modulus of smoothness

DOI10.1134/S0001434614050289zbMath1314.41009MaRDI QIDQ2342045

Konstantin V. Runovski

Publication date: 8 May 2015

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

zbMATH Keywords

modulus of smoothnessHölder's inequalityFourier coefficientFourier meanJackson-type estimate\(2\pi\)-periodic \(p\)th-power integrable function

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Rate of convergence, degree of approximation (41A25)

Related Items (9)

Approximation by Fourier means and generalized moduli of smoothness ⋮ Quality of approximation by Fourier means in terms of general moduli of smoothness ⋮ Approximation by families of generalized sampling series, realizations of generalized \(\mathcal{K} \)-functionals and generalized moduli of smoothness ⋮ On the estimates of the values of various widths of classes of functions of two variables in the weight space \(L_{2, \gamma } ( \mathbb{R}^2)\), \(\gamma = \exp ( - x^2 - y^2)\) ⋮ Some issues of the theory of approximations by entire functions of exponential type and generalized moduli of smoothness ⋮ Mixed generalized modulus of smoothness and approximation by the ``angle of trigonometric polynomials ⋮ Generalized smoothness and approximation of periodic functions in the spaces \(L_p\), \(1 < p < +\infty \) ⋮ Unnamed Item ⋮ Multiplicator type operators and approximation of periodic functions of one variable by trigonometric polynomials

Cites Work

• Approximation by families of linear trigonometric polynomial operators and smoothness properties of functions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A direct theorem of approximation theory for a general modulus of smoothness