Isotonic approximation in \(L_{1}\)

DOI10.1006/jath.2002.3702zbMath1012.41025OpenAlexW2028501106MaRDI QIDQ1867502

Héctor H. Cuenya, Fernando D. Mazzone

Publication date: 2 April 2003

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jath.2002.3702

zbMATH Keywords

monotone approximationsa.e. convergence1-means

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (7)

Characterizing best isotone approximations in \(L_p\) spaces, \(1 \leq p < \infty\) ⋮ A minimizing property of best monotone approximants on their level surfaces ⋮ Extension of the operator of best polynomial approximation in \(L^p(\Omega )\) ⋮ Inequalities in \(L^{p-1}\) for the extended \(L^p\) best approximation operator ⋮ Applications of conditional comonotonicity to some optimization problems ⋮ Extension of the best approximation operator in Orlicz spaces ⋮ Extension of the Best Constant Approximation Operator in Orlicz Spaces

Cites Work

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• Best monotone approximations in \(L_ 1[0,1\)]
• Isotonic approximation in \(L_ s\).
• Strong consistency of multiple isotonic median estimation
• \(L_ \phi\)-approximation by nondecreasing functions on the interval
• Structure of best radial monotone \(\Phi\)-approximants
• Best L 1 -Approximation of L 1 -Approximately Continuous Functions on (0, 1) n by Nondecreasing Functions
• Monotone L 1 -Approximation on the Unit n-Cube
• Best approximants in L ? -spaces
• A Characterization of Best Φ-Approximants
• Continuity of Best Approximants
• Best approximants in L 1 space

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