Self-Equilibrating Sets and Functions in Dual Vector Spaces: Two Boundedness Criteria

This paper is devoted to studying boundedness criteria for extended-real-valued functions. The study is done in the framework of dual vector spaces, using new objects such as self-equilibrated sets and functions. We establish two boundedness new major criteria. The first one says that an extended-real-valued function is bounded below provided it is minorized by an affine map on one of its self-equilibrated subsets. The second criterion says that every self-equilibrated function minorized by an affine mapping on the whole underlying space is bounded below.