Convergence of set-valued mappings: Equi-outer semicontinuity

Adib Bagh, Roger J.B. Wets

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The concept of equi-outer semicontitiuity allows us to relate the pointwise and the graphical convergence of set-valued-mappings. One of the main results is a compactness criterion that extends the classical Arzelà-Ascolì theorem for continuous functions to this new setting; it also leads to the exploration of the notion of continuous convergence. Equi-lower semicontinuity of functions is related to the outer semicontinuity of epigraphical mappings. Finally, some examples involving set-valued mappings are re-examined in terms of the concepts introduced here.

Original languageEnglish
Pages (from-to)333-360
Number of pages28
JournalSet-Valued Analysis
Issue number4
StatePublished - 1996


  • Arzelà-Ascolì theorem
  • Closed convex processes
  • Differential inclusions
  • Epi-convergence
  • Equi-continuity
  • Equi-semicontinuity
  • Maximal monotone
  • Multifunction
  • Operators
  • Set-valued mappings
  • Subgradient mappings
  • Sublinear mappings

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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