Convexity and unique minimum points.

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    • Subject Terms:
      FIXED point theory; BANACH spaces; NORMED rings; CONVEX functions; FUNCTIONAL equations
    • Abstract:
      We show constructively that every quasi-convex, uniformly continuous function f:C→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. [ABSTRACT FROM AUTHOR]
    • Abstract:
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