Volume 7, Number 1, April 2006, pp. 19-37
Andreas Hamel and Andreas Löhne
Key words:
set relations, set-valued variational principle, minimal point theorem, set-valued optimization
Mathematices Subject Classification: 58E30, 46N10
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Copyright© 2006 Yokohama Publishers

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 set-valued maps as well as a minimal point theorem in X × Y and Ekeland's principle for vector-valued functions.

Minimal element theorems and Ekeland's principle with set relations