Journal of Convex Analysis 18 (2011), No. 1, 209--226
Copyright Heldermann Verlag 2011
On the Surjectivity Properties of Perturbations of Maximal Monotone Operators in Non-Reflexive Banach Spaces
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
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.
Keywords: Maximal monotone operators, Fitzpatrick functions, duality mapping, non-reflexive Banach spaces.
MSC: 47H05, 47H14, 49J52, 47N10
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