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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.

Constantin Zalinescu
University "Al. I. Cuza", Faculty of Mathematics, Bd. Copou Nr. 11, 6600 Iasi, Romania

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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