
Journal of Convex Analysis 16 (2009), No. 3, 10111033 Copyright Heldermann Verlag 2009 StronglyRepresentable Monotone Operators Mircea D. Voisei Dept. of Mathematics, Towson University, 7800 York Road, Towson, MD 21252, U.S.A. mvoisei@towson.edu Constantin Zalinescu University "Al. I. Cuza", Faculty of Mathematics, Bd. Copou Nr. 11, 6600 Iasi, Romania zalinesc@uaic.ro Recently M. Marques Alves and B. F. Svaiter ["BrønstedRockafellar property and maximality of monotone operators representable by convex functions in nonreflexive Banach spaces", J. Convex Analysis 15(4) (2008) 693706] introduced a new class of maximal monotone operators. In this note we study domainrange properties as well as connections with other classes and calculus rules for these operators we called stronglyrepresentable. While not every maximal monotone operator is stronglyrepresentable, every maximal monotone NI operator is stronglyrepresentable, and every stronglyrepresentable operator is locally maximal monotone, maximal monotone locally, strongly maximal monotone, and ANA. As a consequence the conjugate of the Fitzpatrick function of a maximal monotone operator is not necessarily a representative function. [ Fulltextpdf (227 KB)] for subscribers only. 