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

In: Fixed-Point Algorithms for Inverse Problems in Science and Engineering

Author

Listed:
  • Liangjin Yao

    (University of British Columbia)

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.

Suggested Citation

  • Liangjin Yao, 2011. "The Brézis-Browder Theorem Revisited and Properties of Fitzpatrick Functions of Order n," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 391-402, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-9569-8_18
    DOI: 10.1007/978-1-4419-9569-8_18
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