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.
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