Simultaneous approximation from convex sets

DOI10.1016/0898-1221(95)00097-6zbMath0842.46011OpenAlexW2049451593MaRDI QIDQ1904172

J. Shi, Robert Huotari

Publication date: 18 December 1995

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(95)00097-6

zbMATH Keywords

\(\ell^ 1\) and \(\ell^ \infty\) vectorial norms\(p\)-strong unicity\(p\)-type modulus of convexityone-sided Gâteaux derivativessimultaneous approximation from convex sets

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Geometry and structure of normed linear spaces (46B20) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (11)

On nonlinear simultaneous approximation problems ⋮ Best \(N\)-simultaneous approximation in \(L_p(\mu, X)\) ⋮ A class of best simultaneous approximation problems ⋮ On nonlinear simultaneous Chebyshev approximation problems. ⋮ Best simultaneous approximation of an infinite set of functions ⋮ Best simultaneous approximation to totally bounded sequences in Banach spaces ⋮ Nonlinear weighted best simultaneous approximation in Banach spaces ⋮ Best Simultaneous Monotone Approximants in Orlicz Spaces ⋮ Uniqueness of simultaneous approximations in continuous function spaces ⋮ Existence of best simultaneous approximations in \(L_p (S,\, \varSigma,\, X)\) ⋮ Existence of best simultaneous approximations in \(L_p(S,\Sigma,X)\) without the RNP assumption

Cites Work

• Local strong uniqueness
• Strongly unique best approximation in uniformly convex Banach spaces
• Relative Chebyshev centers in normed linear spaces. I
• Geometry of Banach spaces. Selected topics
• Uniqueness in vector-valued approximation
• On Best Simultaneous Approximation in Normed Linear Spaces
• Strong unicity versus modulus of convexity
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