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**Berger, Josef and Svindland, Gregor (2019): Convexity and unique minimum points. In: Archive for Mathematical Logic, Vol. 58, No. 1-2: pp. 27-34**

**Full text not available from 'Open Access LMU'.**

## Abstract

We show constructively that every quasi-convex, uniformly continuous function f:CR 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.

Item Type: | Journal article |
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Faculties: | Mathematics, Computer Science and Statistics > Mathematics |

Subjects: | 500 Science > 510 Mathematics |

ISSN: | 0933-5846 |

Language: | English |

Item ID: | 82394 |

Date Deposited: | 15. Dec 2021, 15:01 |

Last Modified: | 15. Dec 2021, 15:01 |