Widths and shape-preserving widths of Sobolev-type classes of \(s\)-monotone functions

DOI10.1016/j.jat.2005.11.016zbMath1096.41019OpenAlexW2058060618MaRDI QIDQ2497226

V. N. Konovalov, Jacek Gilewicz, Dany Leviatan

Publication date: 4 August 2006

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

Full work available at URL: https://doi.org/10.1016/j.jat.2005.11.016

zbMATH Keywords

Sobolev-type classesKolmogorov widthlinear width\(s\)-monotone functions

Mathematics Subject Classification ID

Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (6)

On uniform monotone approximation of continuous monotone functions with the help of translations and dilations of the Laplace integral ⋮ On monotone approximation of piecewise continuous monotone functions with the help of translations and dilations of the Laplace integral ⋮ Approximation by polynomials and ridge functions of classes of \(s\)-monotone radial functions ⋮ Relative widths of smooth functions determined by fractional order derivatives ⋮ Linear relative \(n\)-widths for linear operators preserving an intersection of cones ⋮ The curse of dimensionality for the class of monotone functions and for the class of convex functions

Cites Work

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• Convex functions, partial orderings, and statistical applications
• Free-knot splines approximation of \(s\)-monotone functions
• Shape-preserving widths of weighted Sobolev-type classes of positive, monotone, and convex functions on a finite interval
• Shape preserving widths of Sobolev-type classes of \(s\)-monotone functions on a finite interval.
• A criterion for \(n\)-convexity
• Another Proof that Convex Functions are Locally Lipschitz
• Kolmogorov and linear widths of weighted Sobolev-type classes on a finite interval. II

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