The main result of this paper is a minimal point theorem in a product space \(X\times Y\), where \(X\) is a Hausdorff uniform space and \(Y\) is a topological space. After proving set-valued variants of Ekeland’s variational principle and Caristi’s fixed point theorem the authors show that their minimal point theorem is equivalent to both of these results. Various relationships to other results are also discussed in the paper. The proofs are based on standard tools in set-valued analysis.
For the entire collection see [Zbl 1030.00016].