Minimal convex functions bounded below by the duality product

J. E. Martinez-Legaz, B. F. Svaiter

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)873-878
JournalProceedings of the American Mathematical Society
Volume136
DOIs
Publication statusPublished - 1 Mar 2008

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