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Quasidense monotone multifunctions. (English) Zbl 06861465

Summary: In this paper, we discuss quasidense multifunctions from a Banach space into its dual, and use the two sum theorems proved in a previous paper to give various characterizations of quasidensity, including two fuzzy ones. We investigate the Fitzpatrick extension of such a multifunction. We prove that a closed monotone quasidense multifunction is maximally monotone locally (that is to say, of “type (FPV)”), and strongly maximal. We also prove that a maximally monotone multifunction is quasidense if, and only if, it is locally maximally monotone (that is to say, of “type (FP)”).

MSC:

47H05 Monotone operators and generalizations
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
52A41 Convex functions and convex programs in convex geometry
46A20 Duality theory for topological vector spaces
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