Results 1 to 10 of about 987 (182)

Lebesgue functions and Lebesgue constants in polynomial interpolation [PDF]

Journal of Inequalities and Applications, 2016
The Lebesgue constant is a valuable numerical instrument for linear interpolation because it provides a measure of how close the interpolant of a function is to the best polynomial approximant of the function.
Bayram Ali Ibrahimoglu
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On Lebesgue Constants

Axioms
Simple formulae for Lebesgue constants arising in the classical Fourier series approximation are obtained. Both even and odd cases are addressed, extending Fejér’s results. Asymptotic formulae are also obtained.
Manuel Duarte Ortigueira, Gabriel Bengochea   +1 more
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Sharp Estimates for Lebesgue Constants [PDF]

Proceedings of the American Mathematical Society, 1983
Suppose C ⊂ R N C \subset {R^N} is a closed convex bounded body containing 0 in its interior. If ∂ C \partial C is sufficiently smooth with strictly positive Gauss curvature at each point, then, denoting by
Carenini, M, SOARDI, PAOLO MAURIZIO
openaire   +2 more sources

Matrix Summability of Walsh–Fourier Series

Mathematics, 2022
The presented paper discusses the matrix summability of the Walsh–Fourier series. In particular, we discuss the convergence of matrix transforms in L1 space and in CW space in terms of modulus of continuity and matrix transform variation.
Ushangi Goginava, Károly Nagy
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Sharpness of some Hardy-type inequalities

Journal of Inequalities and Applications, 2023
The current status concerning Hardy-type inequalities with sharp constants is presented and described in a unified convexity way. In particular, it is then natural to replace the Lebesgue measure dx with the Haar measure d x / x $dx/x$ .
Lars-Erik Persson, Natasha Samko, George Tephnadze   +2 more
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Generalized Čebyšev and Grüss Type Results in Weighted Lebesgue Spaces

Mathematics, 2023
The classical Grüss and related inequalities have spurred a range of improvements, refinements, generalizations, and extensions. In the present article, we provide generalizations of Sokolov’s inequality in weighted Lebesgue LωΩ,A,μ spaces by employing ...
Saad Ihsan Butt, Josip Pečarić, Sanja Tipurić-Spužević   +2 more
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Lebesgue Constant Using Sinc Points [PDF]

Advances in Numerical Analysis, 2016
Lebesgue constant for Lagrange approximation at Sinc points will be examined. We introduce a new barycentric form for Lagrange approximation at Sinc points. Using Thiele’s algorithm we show that the Lebesgue constant grows logarithmically as the number of interpolation Sinc points increases.
Maha Youssef, Hany A. El-Sharkawy, Gerd Baumann   +2 more
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Direct and strong converse inequalities for approximation with Fejér means

Demonstratio Mathematica, 2020
We present upper and lower estimates of the error of approximation of periodic functions by Fejér means in the Lebesgue spaces L2πp{L}_{2{\pi }}^{p}. The estimates are given in terms of a K-functional for 1≤p≤∞1\le p\le \infty and in terms of the first ...
Bustamante Jorge
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Sharp Inequalities for the Hardy–Littlewood Maximal Operator on Finite Directed Graphs

Mathematics, 2021
In this paper, we introduce and study the Hardy–Littlewood maximal operator MG→ on a finite directed graph G→. We obtain some optimal constants for the ℓp norm of MG→ by introducing two classes of directed graphs.
Xiao Zhang, Feng Liu, Huiyun Zhang
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Lebesgue constants for Chebyshev thresholding greedy algorithms

Journal of Inequalities and Applications, 2018
We investigate the efficiency of Chebyshev Thresholding Greedy Algorithm (CTGA) for an n-term approximation with respect to general bases in a Banach space. We show that the convergence property of CTGA is better than TGA for non-quasi-greedy bases. Then
Chunfang Shao, Peixin Ye
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