TY - JOUR

T1 - Minimal convex functions bounded below by the duality product

AU - Martinez-Legaz, J. E.

AU - Svaiter, B. F.

PY - 2008/3/1

Y1 - 2008/3/1

N2 - It is well known that the Fitzpatrick function of a maximal monotone operator is minimal in the class of convex functions bounded below by the duality product. Our main result establishes that, in the setting of reflexive Banach spaces, the converse also holds; that is, every such minimal function is the Fitzpatrick function of some maximal monotone operator. Whether this converse also holds in a nonreflexive Banach space remains an open problem. © 2007 American Mathematical Society.

AB - It is well known that the Fitzpatrick function of a maximal monotone operator is minimal in the class of convex functions bounded below by the duality product. Our main result establishes that, in the setting of reflexive Banach spaces, the converse also holds; that is, every such minimal function is the Fitzpatrick function of some maximal monotone operator. Whether this converse also holds in a nonreflexive Banach space remains an open problem. © 2007 American Mathematical Society.

U2 - https://doi.org/10.1090/S0002-9939-07-09176-9

DO - https://doi.org/10.1090/S0002-9939-07-09176-9

M3 - Article

VL - 136

SP - 873

EP - 878

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

ER -