Infinite dimensional generalized Jacobian: Properties and calculus rules

Z. Páles, Vera Zeidan

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The extension to infinite dimensional domains of Clarke's generalized Jacobian is the focus of this paper. First, a generalization of a Fabian-Preiss theorem to the infinite dimensional setting is obtained. As a consequence, a new formula relating the Clarke's generalized Jacobians corresponding to finite dimensional spaces K, L with K ⊆ L is established. Furthermore, in the infinite dimensional case, basic properties pertaining the generalized Jacobian are developed and then an identification of this set-valued map is produced. Applications of these results in the form of chain rules including sum and product rules, and a computational formula for continuous selections are derived.

Original languageEnglish
Pages (from-to)55-75
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume344
Issue number1
DOIs
Publication statusPublished - Aug 1 2008

Fingerprint

Generalized Jacobian
Calculus
Product rule
Continuous Selection
Chain rule
Set-valued Map
K-space
Sum Rules
Theorem

Keywords

  • Chain rule
  • Characterization of the generalized Jacobian
  • Formula for a continuous selection
  • Generalized Jacobian
  • Sum rule

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Infinite dimensional generalized Jacobian : Properties and calculus rules. / Páles, Z.; Zeidan, Vera.

In: Journal of Mathematical Analysis and Applications, Vol. 344, No. 1, 01.08.2008, p. 55-75.

Research output: Contribution to journalArticle

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