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Variational and Extended Sums of Monotone Operators

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Ill-posed Variational Problems and Regularization Techniques

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 477))

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].

This work was completed while the first author was visiting, during the Fall semester 1998, the LACO (Laboratoire d’Arithmétique, Calcul Formel et Optimisation) at the University of Limoges. The same author was also partially supported by the Bulgarian National Fund for Scientific Research under contract No. MM-701/97.

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Author information

Authors and Affiliations

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

    Julian P. Revalski

  2. LACO, Université de Limoges, 123, Avenue Albert Thomas, F-87060, Limoges Cedex, France

    Michel Théra

Authors
  1. Julian P. Revalski
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  2. Michel Théra
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Editor information

Editors and Affiliations

  1. LACO, URA 1586, University of Limoges, 123 Avenue Albert Thomas, 87060, Limoges Cedex, France

    Michel Théra

  2. Fachbereich IV — Mathematik, University of Trier, 54286, Trier, Germany

    Rainer Tichatschke

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© 1999 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/978-3-642-45780-7_14

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  • DOI: https://doi.org/10.1007/978-3-642-45780-7_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66323-2

  • Online ISBN: 978-3-642-45780-7

  • eBook Packages: Springer Book Archive

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