Generalized Jacobian for Functions with Infinite Dimensional Range and Domain

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dc.creatorPáles, Zsolt
dc.creatorZeidan, Vera
dc.date2006-05-30
dc.date.accessioned2026-07-07T07:14:39Z
dc.date.available2026-07-07T07:14:39Z
dc.descriptionIn this paper, locally Lipschitz functions acting between infinite dimensional normed spaces are considered. When the range is a dual space and satisfies the Radon--Nikodým property, Clarke's generalized Jacobian will be extended to this setting. Characterization and fundamental properties of the extended generalized Jacobian are established including the nonemptiness, the $β$-compactness, the $β$-upper semicontinuity, and a mean-value theorem. A connection with known notions is provided and chain rules are proved using key results developed. This included the vectorization and restriction theorem, and the extension theorem. Therefore, the generalized Jacobian introduced in this paper is proved to enjoy all the properties required of a derivative like-set.
dc.identifierhttps://arxiv.org/abs/math/0605771
dc.identifierhttp://arxiv.org/abs/math/0605771
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112966
dc.subjectFunctional Analysis
dc.subject49J52
dc.titleGeneralized Jacobian for Functions with Infinite Dimensional Range and Domain
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