A Note in Approximative Compactness and Continuity of Metric Projections in Banach Spaces

Antonio J. Guirao; Vicente Montesinos

Abstract

We give a counterexample to a recent statement in the metric approximation theory and provide a setting where the statement holds.

Author information

Contact details are reproduced from the original publication and may be historical.

Antonio J. Guirao

Instituto de Matemática Pura y Aplicada, Universidad Politécnica, C/Vera s/n, 46022 Valencia, Spain

anguisa2@mat.upv.es

Vicente Montesinos

Instituto de Matemática Pura y Aplicada, Universidad Politécnica, C/Vera s/n, 46022 Valencia, Spain

vmontesinos@mat.upv.es

Keywords

Metric projection
approximative compactness
midpoint locally uniform rotundity
locally uniform rotundity
C-sets
proximinal sets

Suggested citation

A. J. Guirao, V. Montesinos. “A Note in Approximative Compactness and Continuity of Metric Projections in Banach Spaces.” Journal of Convex Analysis 18 (2011), No. 2, 397–401.