Abstract

Some notions of generalized monotonicity for multi-valued mappings are characterized in terms of properties of the associated Minty variational inequalities. In particular, it is shown that the Minty variational inequality problem derived from a map F defined on a convex domain is solvable on any nonempty, compact, and convex subdomain if and only if F is properly quasimonotone.2000 Mathematics Subject Classification47J2049J4090C26Keywords and phrasesVariational inequalitiesquasimonotonicitypseudomonotonicity

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