Linear-Approximation in l∞n

Finzel, M.

doi:10.1006/jath.1994.1021

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Proof For the Discrete Kolmogorov Criteria1

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Cited by 8 publications

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“…The following lemma states equivalent characterizations of elementary vectors: For the equivalence of (i), (ii), and (iii) see [2], while the equivalence of (iii) and (iv) follows from the following relation, see [3]: Proof. Assume without loss of generality &u& 1 =1.…”

Section: Proof For the Discrete Kolmogorov Criteriamentioning

confidence: 96%

On a Discrete Kolmogorov Criterion

Finzel

2002

Journal of Approximation Theory

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Section: Proof For the Discrete Kolmogorov Criteriamentioning

confidence: 96%

On a Discrete Kolmogorov Criterion

Finzel

2002

Journal of Approximation Theory

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Convergence of Pólya Algorithm and Continuous Metric Selections in Space of Continuous Functions

1995

Journal of Approximation Theory

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Hoffman's Error Bounds and Uniform Lipschitz Continuity of Bestlp-Approximations

Berens

Finzel

et al. 1997

Journal of Mathematical Analysis and Applications

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In a central paper on smoothness of best approximation in 1968 R. Holmes and B. Kripke proved among others that on ‫ޒ‬ n , endowed with the l-norm, 1p-ϱ, p the metric projection onto a given linear subspace is Lipschitz continuous where the Lipschitz constant depended on the parameter p. Using Hoffman's Error Bounds as a principal tool we prove uniform Lipschitz continuity of best l-app proximations. As a consequence, we reprove and prove, respectively, Lipschitz Ž. continuity of the strict best approximation sba, p s ϱ and of the natural best Ž. approximation nba, p s 1 .

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Linear-Approximation in l∞n

Cited by 8 publications

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On a Discrete Kolmogorov Criterion

On a Discrete Kolmogorov Criterion

Convergence of Pólya Algorithm and Continuous Metric Selections in Space of Continuous Functions

Hoffman's Error Bounds and Uniform Lipschitz Continuity of Bestlp-Approximations

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