Best approximation of functions in generalized Hölder class

DOI10.1186/S13660-018-1864-YzbMath1498.41007OpenAlexW2896163170WikidataQ58581286 ScholiaQ58581286MaRDI QIDQ824826

Md. Hadish, Hare Krishna Nigam

Publication date: 15 December 2021

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-018-1864-y

zbMATH Keywords

Fourier seriesbest approximationconjugate Fourier series\(C^1\) means\(TC^1\) meansgeneralized Hölder classmatrix \((T)\) means

Mathematics Subject Classification ID

Matrix methods for summability (40C05) Cesàro, Euler, Nörlund and Hausdorff methods (40G05) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Fourier series and coefficients in several variables (42B05) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (11)

On degree of approximation of Fourier series of functions in Besov space using Nörlund mean ⋮ Degree of convergence of the functions of trigonometric series in Sobolev spaces and its applications ⋮ Degree of convergence of a function in generalized Zygmund space ⋮ Degree of convergence of a function of several variables in generalized Hölder spaces ⋮ Effectiveness of the even-type delayed mean in approximation of conjugate functions ⋮ Degree of convergence of Fourier series in Besov spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Functional approximation in Besov space using generalized Nörlund-Hausdorff product matrix ⋮ Unnamed Item ⋮ Approximation of Fourier Series of Functions in Besov Space by Borel Means

Cites Work

• On the trigonometric approximation of signals belonging to generalized weighted Lipschitz \(W(L^r,\xi(t))(r\geqslant 1)\)-class by matrix \((C^1\cdot N_p)\) operator of conjugate series of its Fourier series
• Using infinite matrices to approximate functions of class Lip\((\alpha ,p)\) using trigonometric polynomials
• Degree of approximation of functions \(\tilde f \in H_\omega\) class by the \((N_p \cdot E^1)\) means in the Hölder metric
• Product \((N,p_n)(C,1)\) summability of a sequence of Fourier coefficients
• Trigonometric approximation of periodic Signals belonging to generalized weighted Lipschitz W'(L_r,ξ(t)),(r≥1) -- class by Nörlund-Euler (N,p_n) (E,q) operator of conjugate series of its Fourier series
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