Journal of Convex Analysis 16 (2009), No. 3, 1011--1033
Copyright Heldermann Verlag 2009
Strongly-Representable 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 ["Brønsted-Rockafellar property and maximality of monotone operators representable by convex functions in non-reflexive Banach spaces", J. Convex Analysis 15(4) (2008) 693--706] introduced a new class of maximal monotone operators. In this note we study domain-range properties as well as connections with other classes and calculus rules for these operators we called strongly-representable. While not every maximal monotone operator is strongly-representable, every maximal monotone NI operator is strongly-representable, and every strongly-representable 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.
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