LC-functions and maximal monotonicity
Stephen Simons · 2005
In this paper, we consider LC‐functions, a class of special convex functions from the product of a reflexive Banach space and its dual into ]1 ,1]. Using Fitzpatrick functions, we will show that the theory of LC‐functions is a proper extension of the theory of maximal monotone sets. Various versons of the Fenchel duality theorem lead to a number of results on maximal monotonicity, some of them new. In particular, we prove various surjectivity results, including a generalization of a known “abstract Hammerstein theorem”, give sucient conditions for a sum of maximal monotone multifunctions to be maximal monotone, and prove a generalization of the Brezis‐Haraux theorem