Fixed points in the family of convex representations of a maximal monotone operator

Svaiter, B.

doi:10.1090/S0002-9939-03-07083-7

Fixed points in the family of convex representations of a maximal monotone operator
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Proc. Amer. Math. Soc. 131 (2003), 3851-3859 Request permission

Abstract:

Any maximal monotone operator can be characterized by a convex function. The family of such convex functions is invariant under a transformation connected with the Fenchel-Legendre conjugation. We prove that there exists a convex representation of the operator which is a fixed point of this conjugation.

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