On some concepts of generalized differentials

Benedetto Piccoli, Ewa Girejko

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this paper, we study some concepts of generalized differentials for set-valued maps and introduce some new ones. In particular we first focus on the concept of Generalized Differential Quotients, briefly GDQs. It is shown that minimal GDQs are unique for scalar single-valued functions, then GDQs are compared with contingent and Dini derivatives, finally some other results characterizing GDQs are given. A new definition of generalized differentiation theory is presented, namely weak GDQs that are a modification of GDQs. We clarify the relationships with other concepts of generalized differentiability: Clarke generalized Jacobians, path-integral generalized differentials and Warga derivate containers. Finally, some applications of GDQs end the paper.

Original languageEnglish (US)
Pages (from-to)163-183
Number of pages21
JournalSet-Valued Analysis
Issue number2
StatePublished - Jun 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


  • CCA set-valued maps
  • Generalized differential quotients
  • Minimal generalized differential quotients

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