On the Surjectivity Properties of Perturbations of Maximal Monotone Operators in Non-Reflexive Banach Spaces

Maicon Marques Alves; Benar Fux Svaiter

Abstract

We are concerned with surjectivity of perturbations of maximal monotone operators in non-reflexive Banach spaces. While in a reflexive setting, a classical surjectivity result due to Rockafellar gives a necessary and sufficient condition to maximal monotonicity, in a non-reflexive space we characterize maximality using an "enlarged" version of the duality mapping, introduced previously by Gossez.

Author information

Contact details are reproduced from the original publication and may be historical.

Maicon Marques Alves

Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil

maicon@impa.br

Benar Fux Svaiter

Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro, RJ 22460-320, Brazil

benar@impa.br

Keywords

Maximal monotone operators
Fitzpatrick functions
duality mapping
non-reflexive Banach spaces

Mathematics Subject Classification

47H05, 47H14, 49J52, 47N10

Suggested citation

M. Marques Alves, B. F. Svaiter. “On the Surjectivity Properties of Perturbations of Maximal Monotone Operators in Non-Reflexive Banach Spaces.” Journal of Convex Analysis 18 (2011), No. 1, 209–226.