
Journal of Convex Analysis 10 (2003), No. 2, 465475 Copyright Heldermann Verlag 2003 Continuity and Maximality Properties of Pseudomonotone Operators Nicolas Hadjisavvas Dept. of Product and Systems Design, University of the Aegean, 84100 Hermoupolis, Syros, Greece, nhad@aegean.gr Given a Banach space X, a multivalued operator T: X > 2^{X*} is called pseudomonotone (in Karamardian's sense) if for all (x, x*) and (y, y*) in its graph, <x*, y  x> ≥ 0 implies <y*, y  x> ≥ 0. We define an equivalence relation on the set of pseudomonotone operators. Based on this relation, we define a notion of "Dmaximality" and show that the Clarke subdifferential of a locally Lipschitz pseudoconvex function is Dmaximal pseudomonotone. We generalize some wellknown results on upper semicontinuity and generic singlevaluedness of monotone operators by showing that, under suitable assumptions, a pseudomonotone operator has an equivalent operator that is upper semicontinuous, generically singlevalued etc. Keywords: maximal monotone operator, pseudomonotone operator, pseudoconvex function. MSC 2000: 26B25, 47H04, 47H05. FullTextpdf (336 KB) 