Abstract

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.

Author information

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

Orestes Bueno

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

obueno@imca.edu.pe

Yboon García

Centro de Investigación, Universidad del Pacífico, Av. Salaverry 2020, Lima, Perú

garcia_yv@up.edu.pe

Maicon Marques Alves

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

maicon.alves@ufsc.br

Keywords

  • Banach spaces
  • Monotone operators
  • Variational Sum
  • Variational Composition
  • Type (D) operators
  • Moreau-Yosida regularization

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Suggested citation

O. Bueno, Y. García, M. Marques Alves. “Lower Limits of Type (D) Monotone Operators in General Banach Spaces.” Journal of Convex Analysis 23 (2016), No. 2, 333–345. https://doi.org/10.68381/jca23013

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Published by Heldermann Verlag, 2016. Rights now held by Banach Press LLC.