Geodesic
The Fitzpatrick Rate, the Stepanov Rate, the Lipschitz Rate and their Relatives
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 839-848
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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.
Classification : 26B05
Mots-clés : Best approximation, derivative, distance function, Fitzpatrick rate, Lipschitz rate, stability, Stepanov rate, subdifferential 
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     author = {J.-P. Penot},
     title = {The {Fitzpatrick} {Rate,} the {Stepanov} {Rate,} the {Lipschitz} {Rate} and their {Relatives}},
     journal = {Journal of convex analysis},
     pages = {839--848},
     year = {2006},
     volume = {13},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a22/}
}
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J.-P. Penot. The Fitzpatrick Rate, the Stepanov Rate, the Lipschitz Rate and their Relatives. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 839-848. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a22/