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Journal of Convex Analysis 23 (2016), No. 2, 333--345
Copyright Heldermann Verlag 2016

Lower Limits of Type (D) Monotone Operators in General Banach Spaces

Orestes Bueno
Instituto de Matemática y Ciencias Afines, Calle Los Biológos 245, La Molina, Lima 12, Perú

Yboon García
Centro de Investigacion, Universidad del Pacífico, Av. Salaverry 2020, Lima, Perú

Maicon Marques Alves
Dep. de Matemática, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, Brazil

We give, for general Banach spaces, a characterization of the sequential lower limit of maximal monotone operators of type (D) and prove its representability. As a consequence, using a recent extension of the Moreau-Yosida regularization for type (D) operators, we extend to general Banach spaces the definitions of the variational sum of monotone operators and the variational composition of monotone operators with continuous linear mappings, and we prove that both operators are representable.

Keywords: Banach spaces, Monotone operators, Variational Sum, Variational Composition, Type (D) operators, Moreau-Yosida regularization.

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