Phelps ' Lemma , Dane s ' Drop Theorem and Ekeland ' sPrinciple in Locally Convex
نویسندگان
چکیده
We present a generalization of the Phelps lemma to locally convex topological vector spaces and show the equivalence of this theorem, Ekeland's principle and Dane s' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto eeciency theorem due to Isac. Concerning the drop theorem this solves a problem proposed by G. Isac in 1997. We show that another formulation of Ekeland's principle in locally convex spaces using a family of topology generating semi-norms as perturbation functions rather than a single (in general discontinuous) Minkowski functional turns out to be equivalent to the original version.
منابع مشابه
Phelps’ Lemma, Danes̆’ Drop Theorem and Ekeland’s Principle in Locally Convex Spaces
A generalization of Phelps’ lemma to locally convex spaces is proven, applying its well-known Banach space version. We show the equivalence of this theorem, Ekeland’s principle and Danes̆’ drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto efficiency theorem due to Isac. This solves a problem, concerning the drop theorem, proposed by G. Isac in 1997. We show...
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