Journal of Convex Analysis 19 (2012), No. 2, 575--589
Copyright Heldermann Verlag 2012
A New Qualification Condition for the Maximality of the Sum of Maximal Monotone Operators in General Banach Spaces
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
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.
Keywords: Maximal monotone operators, sum, nonreflexive Banach spaces, Fitzpatrick functions.
MSC: 47H05, 49J52, 47N10
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