Convexity and unique minimum points

Berger, Josef und Svindland, Gregor (2019): Convexity and unique minimum points. In: Archive for Mathematical Logic, Bd. 58, Nr. 1-2: S. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0933-5846
• Sprache: Englisch