Set-Valued Analysis

, Volume 7, Issue 2, pp 117-132

ε-Enlargements of Maximal Monotone Operators in Banach Spaces

  • Regina Sandra BurachikAffiliated withEngenharia de Sistemas e Computação, COPPE–UFRJ
  • , B. F. SvaiterAffiliated withInstituto de Matemática Pura e Aplicada, IMPA

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Given a maximal monotone operator T in a Banach space, we consider an enlargement Tε, in which monotonicity is lost up to ε, in a very similar way to the ε-subdifferential of a convex function. We establish in this general framework some theoretical properties of Tε, like a transportation formula, local Lipschitz continuity, local boundedness, and a Brøndsted–Rockafellar property.

Banach spaces maximal monotone operators enlargement of an operator Brøndsted–Rockafellar property transportation formula Lipschitz continuity local boundedness