ISSN:
1572-932X
Keywords:
54C60
;
54B20
;
49J40
;
49J52
;
set-valued mappings
;
epi-convergence
;
multifunction
;
equi-continuity
;
equi-semicontinuity
;
Arzelà-Ascolì theorem
;
maximal monotone
;
operators
;
differential inclusions
;
closed convex processes
;
sublinear mappings
;
subgradient mappings
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The concept of equi-outer semicontinuity 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00436110
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