Set-Valued Analysis

, Volume 8, Issue 4, pp 311–328

A Family of Enlargements of Maximal Monotone Operators

  • B. F. Svaiter

DOI: 10.1023/A:1026555124541

Cite this article as:
Svaiter, B.F. Set-Valued Analysis (2000) 8: 311. doi:10.1023/A:1026555124541


We introduce a family of enlargements of maximal monotone operators. The Brønsted and Rockafellar ε-subdifferential operator can be regarded as an enlargement of the subdifferential. The family of enlargements introduced in this paper generalizes the Brønsted and Rockafellar ε-subdifferential (enlargement) and also generalize the enlargement of an arbitrary maximal monotone operator recently proposed by Burachik, Iusem and Svaiter. We characterize the biggest and the smallest enlargement belonging to this family and discuss some general properties of its members. A subfamily is also studied, namely the subfamily of those enlargements which are also additive. Members of this subfamily are formally closer to the ε-subdifferential. Existence of maximal elements is proved. In the case of the subdifferential, we prove that the ε-subdifferential is maximal in this subfamily.

maximal monotone operators enlargements Banach spaces 

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • B. F. Svaiter
    • 1
  1. 1.IMPA, Instituto de Matemática Pura e AplicadaRio de Janeiro, RJBrazil

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