Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Jean-Pierre Crouzeix

LIMOS, Campus Scientifique des Cézeaux, Université Blaise Pascal, 63170 Aubière, France

jp.crouzeix@isima.fr

Eladio Ocaña Anaya

IMCA, Universidad Nacional de Ingeniería, Calle Los Biólogos 245, Urb. San Cesar, La Molina – Lima 12, Peru

eocana@imca.edu.pe

Keywords

  • Monotonicity
  • maximal monotonicity
  • variational inequality problems
  • generalized equilibrium problems

Suggested citation

J.-P. Crouzeix, E. Ocaña Anaya. “Maximality is Nothing But Continuity.” Journal of Convex Analysis 17 (2010), No. 2, 521–534.

Copyright Banach Press 2010