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Convexity and unique minimum points

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Abstract

We show constructively that every quasi-convex, uniformly continuous function \(f:C \rightarrow \mathbb {R}\) with at most one minimum point has a minimum point, where C is a convex compact subset of a finite dimensional normed space. Applications include a result on strictly quasi-convex functions, a supporting hyperplane theorem, and a short proof of the constructive fundamental theorem of approximation theory.

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Authors and Affiliations

  1. Department of Mathematics, LMU Munich, Munich, Germany

    Josef Berger & Gregor Svindland

Authors
  1. Josef Berger
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  2. Gregor Svindland
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Correspondence to Josef Berger.

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Berger, J., Svindland, G. Convexity and unique minimum points. Arch. Math. Logic 58, 27–34 (2019). https://doi.org/10.1007/s00153-018-0619-2

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  • DOI: https://doi.org/10.1007/s00153-018-0619-2

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