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Generalized Jacobian for Functions with Infinite Dimensional Range and Domain

Zsolt Páles·Vera Zeidan
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Abstract

In 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.

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BibTeXRIS

Zsolt Páles, Vera Zeidan. 2006-05-30. Generalized Jacobian for Functions with Infinite Dimensional Range and Domain. https://arxiv.org/abs/math/0605771

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