Abstract

We study maximal monotonicity of the sum of maximal monotone operators in general Banach spaces. Under certain qualification condition (QC) on the domain of Fitzpatrick convex representations of the operators the sum is maximal monotone, even in nonreflexive Banach spaces.

Author information

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Maicon Marques Alves

Dep. de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, 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
  • sum
  • nonreflexive Banach spaces
  • Fitzpatrick functions

Mathematics Subject Classification

47H05, 49J52, 47N10

References

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Suggested citation

M. Marques Alves, B. F. Svaiter. “A New Qualification Condition for the Maximality of the Sum of Maximal Monotone Operators in General Banach Spaces.” Journal of Convex Analysis 19 (2012), No. 2, 575–589. https://doi.org/10.68381/jca19032

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press.