\(L_ p\) approximation by quasi-convex and convex functions

DOI10.1016/0022-247X(89)90130-3zbMath0673.41030OpenAlexW1965317052MaRDI QIDQ1120770

Vasant A. Ubhaya

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0022-247x(89)90130-3

zbMATH Keywords

quasi-convex functionsbest \(L_ p\)-approximation

Mathematics Subject Classification ID

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

Related Items (3)

Characterizing best isotone approximations in \(L_p\) spaces, \(1 \leq p < \infty\) ⋮ \(L_ p\) approximation by subsets of convex functions of several variables ⋮ \(L_ p\)-approximation from nonconvex subsets of special classes of functions

Cites Work

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• Uniform approximation by quasi-convex and convex functions
• Lipschitz condition in minimum norm problems on bounded functions
• Quasi-convex optimization
• An O(n) algorithm for least squares quasi-convex approximation
• Isotonic approximation in \(L_ s\).
• Natural choice of \(L_ 1-\)approximants
• \(L_p\) convergence of monotone functions and their uniform convergence
• \(L_ p\) approximation by subsets of convex functions of several variables
• \(L_ p\)-approximation from nonconvex subsets of special classes of functions
• Best approximants in L 1 space
• Another Proof that Convex Functions are Locally Lipschitz
• Almost everywhere convergence of prediction sequence in L p (1 < p < ?)
• Seven Kinds of Convexity
• Additively decomposed quasiconvex functions

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