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

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

2008-02-10

arxiv.org/abs/0802.1347v2

Proceedings of the American Mathematical Society, 131 (2003), n. 12, 3851-3859

Mathematics

Functional Analysis

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

Scientific paper

10.1090/S0002-9939-03-07083-7

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.

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