Variational and Extended Sums of Monotone Operators

  • Julian P. Revalski
  • Michel Théra
Conference paper

DOI: 10.1007/978-3-642-45780-7_14

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 477)
Cite this paper as:
Revalski J.P., Théra M. (1999) Variational and Extended Sums of Monotone Operators. In: Théra M., Tichatschke R. (eds) Ill-posed Variational Problems and Regularization Techniques. Lecture Notes in Economics and Mathematical Systems, vol 477. Springer, Berlin, Heidelberg

Abstract

In this article we show that the notion of variational sum of maximal monotone operators, introduced by Attouch, Baillon and Théra in [3] in the setting of Hilbert spaces, can be successfully extended to the case of reflexive Banach spaces, preserving all of its properties. We make then a comparison with the usual pointwise sum and with the notion of extended sum proposed in our paper [26].

Keywords

monotone operators sums of operators enlargements Yosida regularizations subdifferentials 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Julian P. Revalski
    • 1
  • Michel Théra
    • 2
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.LACOUniversité de LimogesLimoges CedexFrance

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