Abstract

We study extended notions for sums of monotone operators and for precompositions of monotone operators with continuous linear mappings. First, we establish some new properties related to the notion of extended sum recently proposed by Revalski and Théra, among them the monotonicity of this sum provided the operators involved are maximal monotone. Then, we show that the equivalence which exists between usual sums and compositions remains valid also for the extended operations. This allows us to obtain some known and new results for extended compositions via the corresponding properties of extended sums.

Author information

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

Yboon García

Université des Antilles et de la Guyane, Campus de Fouillole, 97159 Pointe-à-Pitre, Guadeloupe, France

yboon.garcia@univ-ag.fr

Marc Lassonde

Université des Antilles et de la Guyane, Campus de Fouillole, 97159 Pointe-à-Pitre, Guadeloupe, France

marc.lassonde@univ-ag.fr

Julian P. Revalski

Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Street Block 8, 1113 Sofia, Bulgaria

revalski@math.bas.bg

Keywords

  • Monotone operators
  • extended sums of monotone operators
  • compositions
  • enlargements
  • subdifferentials

Mathematics Subject Classification

47H05, 52A41, 26B25

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Suggested citation

Y. García, M. Lassonde, J. P. Revalski. “Extended Sums and Extended Compositions of Monotone Operators.” Journal of Convex Analysis 13 (2006), No. 3/4, 721–738. https://doi.org/10.68381/jca13054

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Published by Heldermann Verlag, 2006. Rights now held by Banach Press LLC.