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Journal of Convex Analysis 13 (2006), No. 3, 839--848
Copyright Heldermann Verlag 2006

The Fitzpatrick Rate, the Stepanov Rate, the Lipschitz Rate and their Relatives

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

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.

Keywords: Best approximation, derivative, distance function, Fitzpatrick rate, Lipschitz rate, stability, Stepanov rate, subdifferential.

MSC: 26B05

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