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Journal of Convex Analysis 17 (2010), No. 2, 521--534
Copyright Heldermann Verlag 2010

Maximality is Nothing But Continuity

Jean-Pierre Crouzeix
LIMOS, Campus Scientifique des Cézeaux, Université Blaise Pascal, 63170 Aubière, France

Eladio Ocaña Anaya
IMCA, Universidad Nacional de Ingeniería, Calle Los Biólogos 245, Urb. San Cesar, La Molina -- Lima 12, Peru

We show the connexions between the maximality of a monotone set-valued mapping and some continuity conditions on the domain of the mapping and on the mapping itself. We provide an original and simple proof of the famous characterization of maximal monotone mapping of Minty. Some words are said on monotone variational and generalized equilibrium problems.

Keywords: Monotonicity, maximal monotonicity, variational inequality problems, generalized equilibrium problems.

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