Minimal element theorems and Ekeland's principle with set relations
Subject
Set relations; Setvalued variational principle; Minimal point theorem; Setvalued optimization
We present two existence principles for minimal points of subsets of the product space X × 2Y, where X stands for a separated uniform space and Y a topological vector space. The two principles are distinct with respect to the involved ordering structure in 2Y.
We derive from them new variants of Ekeland's principle for setvalued maps as well as a minimal point theorem in X × Y and Ekeland's principle for vectorvalued functions.
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