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
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.
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