Generalized Jacobian for Functions with Infinite Dimensional Range and Domain

Details Generalized Jacobian for Functions with Infinite Dimensional Range and Domain Generalized Jacobian for Functions with Infinite Dimensional Range and Domain

2006-05-30

arxiv.org/abs/math/0605771v1

Mathematics

Functional Analysis

Scientific paper

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--Nikod\'ym 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 $\beta$-compactness, the $\beta$-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.

Affiliated with

Also associated with

No associations

Rating

Generalized Jacobian for Functions with Infinite Dimensional Range and Domain does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized Jacobian for Functions with Infinite Dimensional Range and Domain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized Jacobian for Functions with Infinite Dimensional Range and Domain will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-711386