Abstract
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 language | English |
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Pages (from-to) | 333-360 |
Number of pages | 28 |
Journal | Set-Valued Analysis |
Volume | 4 |
Issue number | 4 |
DOIs | |
State | Published - 1996 |
Keywords
- 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