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On totally Fenchel unstable functions in finite dimensional spaces

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Abstract

We give an answer to the Problem 11.6 posed by Stephen Simons in his book “From Hahn-Banach to Monotonicity”: Do there exist a nonzero finite dimensional Banach space and a pair of extended real-valued, proper and convex functions which is totally Fenchel unstable? The answer is negative.

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References

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Authors and Affiliations

  1. Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Radu Ioan Boţ

  2. Institute of Mathematics, Martin Luther University Halle–Wittenberg, 06099, Halle, Germany

    Andreas Löhne

Authors
  1. Radu Ioan Boţ
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  2. Andreas Löhne
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Correspondence to Radu Ioan Boţ.

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Boţ, R.I., Löhne, A. On totally Fenchel unstable functions in finite dimensional spaces. Math. Program. 123, 25–31 (2010). https://doi.org/10.1007/s10107-009-0311-8

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  • DOI: https://doi.org/10.1007/s10107-009-0311-8

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