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

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 exist a convex representation of the operator which is a fixed point of this conjugation.

13 pages, updated references. Submited in July 2002 to Proc. AMS