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New concept of the ABB theorem. (Nouvelle approche du théorème de ABB.) (French) Zbl 1167.49020
Summary: This note presents a density result of the Arrow-Barankin-Blackwell (ABB) theorem type for a strong topology of a Banach space equipped with the preorder associated to a convex well-based cone. The hypothesis of compactness is relaxed. Here the technique used is based on properties of the Bishop-Phelps cone, and does not require any property of the Hening dilating cone.
MSC:
49J99 Existence theories in calculus of variations and optimal control
46N10 Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
90C48 Programming in abstract spaces
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