arXiv:0802.1347 Abstract | arXiv Analytics

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

Published 2008-02-10, updated 2008-02-12Version 2

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.

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

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

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

Categories: math.FA

Subjects: 47H05, 47H04, 46B99

Keywords: maximal monotone operator, convex representation, fixed point, convex function

Tags: journal article

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