Journal Home Page

Cumulative Index

List of all Volumes

Complete Contents
of this Volume

Previous Article

Next Article

Journal of Convex Analysis 27 (2020), No. 3, 923--934
Copyright Heldermann Verlag 2020

The Lipschitz Condition of the Metric Projection in the Plis Metric

Maxim V. Balashov
V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow 117997, Russia

We consider the class of Banach spaces where the metric projection on a convex closed bounded set is Lipschitz continuous in the Plis metric with respect to the set. We obtain some geometrical and analytical conditions for this property. In fact, the space should has a Hilbert-like structure.

Keywords: Uniform convexity, uniform smoothness, Banach space, Hilbert space, metric projection, Plis metric, moduli of convexity and smoothness.

MSC: 49J53, 52A07, 46C05, 26B25; 46B25, 46B20.

[ Fulltext-pdf  (112  KB)] for subscribers only.