Geodesic
The Core of the Infinite Dimensional Generalized Jacobian
Journal of convex analysis, Tome 16 (2009) no. 2, pp. 321-349

Voir la notice de l'article provenant de la source Heldermann Verlag

Locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon-Nikodym property, a generalized core-Jacobian, Δ f(p) is introduced, and its fundamental properties are established. Primarily, it is shown that the β-closure of its convex hull is exactly the generalized Jacobian. Furthermore, the nonemptiness, the β-compactness, the β-upper semicontinuity, and even another representation are obtained. Connections with known notions are derived and chain rules are proved using key results developed. Therefore, the generalized core-Jacobian introduced in this paper is proved to enjoy all the properties that allow this set to be the nucleus of the generalized Jacobian.
Classification : 49J52, 49A52, 58C20
Mots-clés : Generalized Jacobian 
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     author = {Z. P\'ales and V. Zeidan},
     title = {The {Core} of the {Infinite} {Dimensional} {Generalized} {Jacobian}},
     journal = {Journal of convex analysis},
     pages = {321--349},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2009},
     url = {http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a0/}
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Z. Páles; V. Zeidan. The Core of the Infinite Dimensional Generalized Jacobian. Journal of convex analysis, Tome 16 (2009) no. 2, pp. 321-349. http://geodesic.mathdoc.fr/item/JCA_2009_16_2_JCA_2009_16_2_a0/