LC-functions and maximal monotonicity
نویسنده
چکیده
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 ]−∞,∞]. 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 sufficient conditions for a sum of maximal monotone multifunctions to be maximal monotone, and prove a generalization of the Brezis–Haraux theorem
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