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