Hoffman’s Error Bounds and Uniform Lipschitz Continuity of Best l(p) -Approximations

Authors

H. Berens
M. Finzel
W. Li, Old Dominion University
Y. Xu

Document Type

Article

Publication Date

1997

DOI

10.1006/jmaa.1997.5521

Publication Title

Journal of Mathematical Analysis and Applications

Volume

213

Issue

1

Pages

183-201

Abstract

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 l_ρ-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 l_ρ -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.

Comments

Web of Science: "Free full-text from publisher."

Copyright © 1997 by Academic Press.

Original Publication Citation

Berens, H., Finzel, M., Li, W., & Xu, Y. (1997). Hoffman's error bounds and uniform lipschitz continuity of best l_p-approximations. Journal of Mathematical Analysis and Applications, 213(1), 183-201. doi:10.1006/jmaa.1997.5521

Repository Citation

Berens, H.; Finzel, M.; Li, W.; and Xu, Y., "Hoffman’s Error Bounds and Uniform Lipschitz Continuity of Best l(p) -Approximations" (1997). Mathematics & Statistics Faculty Publications. 86.
https://digitalcommons.odu.edu/mathstat_fac_pubs/86