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Full-Text Articles in Physical Sciences and Mathematics
Hoffman’S Error Bounds And Uniform Lipschitz Continuity Of Best L(P) -Approximations, H. Berens, M. Finzel, W. Li, Y. Xu
Hoffman’S Error Bounds And Uniform Lipschitz Continuity Of Best L(P) -Approximations, H. Berens, M. Finzel, W. Li, Y. Xu
Mathematics & Statistics Faculty Publications
In a central paper on smoothness of best approximation in 1968 R. Holmes and B. Kripke proved among others that on ℝn, endowed with the lρ-norm, 1< 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 lρ -ap- proximations. As a consequence, we reprove and prove, respectively, Lipschitz. continuity of the strict best approximation (sba, p = ∞ and of the natural best approximation (nba, p = 1.