Uniform Lipschitz Continuity of Best l(p)-approximations by Polyhedral Sets

Authors

Martina Finzel
Wu Li, Old Dominion University

Document Type

Article

Publication Date

1998

DOI

10.1006/jmaa.1998.6120

Publication Title

Journal of Mathematical Analysis and Applications

Volume

228

Issue

1

Pages

112-118

Abstract

In this paper we prove that the metric projection Π_{k, p} onto a polyhedral subset K of ℝⁿ, endowed with the p-norm, is uniformly Lipschitz continuous with respect to p,1 , p , ∞. As a consequence the strict best approximation and the natural best approximation are Lipschitz continuous selections for the metric projections Π_k, _∞ and Π_k,1, respectively. This extends a recent analogous result in Berens et al. [J.Math. Anal. Appl. 213 1997, 183-201] on linear subspaces.

Comments

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

Copyright © 1998 by Academic Press.

Original Publication Citation

Finzel, M., & Li, W. (1998). Uniform Lipschitz continuity of best l_p-approximations by polyhedral sets. Journal of Mathematical Analysis and Applications, 228(1), 112-118. doi:10.1006/jmaa.1998.6120

Repository Citation

Finzel, Martina and Li, Wu, "Uniform Lipschitz Continuity of Best l(p)-approximations by Polyhedral Sets" (1998). Mathematics & Statistics Faculty Publications. 87.
https://digitalcommons.odu.edu/mathstat_fac_pubs/87