Abstract

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.

Author information

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

Maxim V. Balashov

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

balashov73@mail.ru

Keywords

  • Uniform convexity
  • uniform smoothness
  • Banach space
  • Hilbert space
  • metric projection
  • Plis metric
  • moduli of convexity and smoothness

Mathematics Subject Classification

49J53, 52A07, 46C05, 26B25; 46B25, 46B20

Suggested citation

M. V. Balashov. “The Lipschitz Condition of the Metric Projection in the Plis Metric.” Journal of Convex Analysis 27 (2020), No. 3, 923–934.

Copyright Heldermann Verlag 2020