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Archive for Mathematical Logic

, Volume 58, Issue 1–2, pp 27–34 | Cite as

Convexity and unique minimum points

  • Josef BergerEmail author
  • Gregor Svindland
Article
  • 37 Downloads

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.

Keywords

Bishop’s constructive mathematics Convex sets and functions Supporting hyperplanes Approximation theory 

Mathematics Subject Classification

03F60 52A41 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsLMU MunichMunichGermany

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