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