Abstract

We give some variants of a constant associated to a real-valued function on a Banach space and a point of the space, as introduced by S. Fitzpatrick. Some of them have a one-sided character and enable to give criteria of subdifferentiability (or differentiability) of different types. An application to best approximation is presented.

Author information

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

Jean-Paul Penot

Lab. de Mathématiques, CNRS UMR 5142, Faculté des Sciences, Av. de l'Université, 64000 Pau, France

Jean-Paul.Penot@univ-pau.fr

Keywords

  • Best approximation
  • derivative
  • distance function
  • Fitzpatrick rate
  • Lipschitz rate
  • stability
  • Stepanov rate
  • subdifferential

Mathematics Subject Classification

26B05

Suggested citation

J.-P. Penot. “The Fitzpatrick Rate, the Stepanov Rate, the Lipschitz Rate and their Relatives.” Journal of Convex Analysis 13 (2006), No. 3/4, 839–848.

Copyright Heldermann Verlag 2006