Document Type

Article

Publication Date

1997

DOI

10.1006/jath.1996.3018

Publication Title

Journal of Approximation Theory

Volume

90

Issue

3

Pages

319-339

Abstract

We discuss the geometric characterization of a subset K of a normed linear space via continuity conditions on the metricprojection onto K. The geometric properties considered includeconvexity, tubularity, and polyhedral structure. The continuityconditions utilized include semicontinuity, generalized stronguniqueness and the non-triviality of the derived mapping. Infinite-dimensional space with the uniform norm we show thatconvexity is equivalent to rotation-invariant almost convexityand we characterize those sets every rotation of which has continuousmetric projection. We show that polyhedral structure underliesgeneralized strong uniqueness of the metric projection.

Comments

Elsevier open archive. Copyright © 1997 Academic Press. All rights reserved.

Original Publication Citation

Huotari, R., & Li, W. (1997). Continuities of metric projection and geometric consequences. Journal of Approximation Theory, 90(3), 319-339. doi:10.1006/jath.1996.3018

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