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The Rockafellar Conjecture and type (FPV)

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The Original Article was published on 12 March 2014

Abstract

In this note, using a technique of Verona and Verona, we show that a result announced in “All maximal monotone operators in a Banach space are of type FPV” by A. Eberhard and R. Wenczel, Set-Valued Var. Anal. 22, 597–615, (2014), implies the truth of the Rockafellar conjecture. We then show that there is a gap in the logic of the Eberhard–Wenczel result, which we tried unsuccessfully to close. We also discuss briefly the connection with maximally monotone multifunctions of type (FPV).

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References

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Radu Ioan Boţ

  2. Universidad del Pacífico Jr. Gral. Sanchez Cerro 2050, Pabellón I Jesús María, Lima 11, Perú

    Orestes Bueno

  3. Department of Mathematics, University of California, Santa Barbara, CA, 93106-3080, USA

    Stephen Simons

Authors
  1. Radu Ioan Boţ
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  2. Orestes Bueno
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  3. Stephen Simons
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Corresponding author

Correspondence to Stephen Simons.

Additional information

The Editor in Chief thanks the authors of the note for pointing out the problem in the publication by Eberhard and Wenczel.

This comment refers to the article available at: http://dx.doi.org/10.1007/s11228-014-0275-6.

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Boţ, R.I., Bueno, O. & Simons, S. The Rockafellar Conjecture and type (FPV). Set-Valued Var. Anal 24, 381–385 (2016). https://doi.org/10.1007/s11228-016-0384-5

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  • DOI: https://doi.org/10.1007/s11228-016-0384-5

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