The Brézis-Browder Theorem Revisited and Properties of Fitzpatrick Functions of Order n

Liangjin Yao ()
Additional contact information
Liangjin Yao: University of British Columbia

Chapter Chapter 18 in Fixed-Point Algorithms for Inverse Problems in Science and Engineering, 2011, pp 391-402 from Springer

Abstract: Abstract In this paper, we study maximal monotonicity of linear relations (set-valued operators with linear graphs) on reflexive Banach spaces. We provide a new and simpler proof of a result due to Brézis–Browder which states that a monotone linear relation with closed graph is maximal monotone if and only if its adjoint is monotone. We also study Fitzpatrick functions and give an explicit formula for Fitzpatrick functions of order n for monotone symmetric linear relations.

Keywords: Adjoint; Convex function; Convex set; Fenchel conjugate; Fitzpatrick function; Linear relation; Maximal monotone operator; Multifunction; Monotone operator; Set-valued operator; Symmetric operator. (search for similar items in EconPapers)
Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-9569-8_18

Ordering information: This item can be ordered from
http://www.springer.com/9781441995698

DOI: 10.1007/978-1-4419-9569-8_18

Access Statistics for this chapter

More chapters in Springer Optimization and Its Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().