Convexity and unique minimum points

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

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
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0933-5846
• Language: English