Inverse maximum theorems and some consequences

Abstract

We deal with direct and inverse maximum theorems. Alternative versions to the Berge theorem are provided, by relaxing the compactness condition of the constraint correspondence. These variants allow us to generalize a result by Terazono and Matani. Also, inverse maximum theorems are introduced. These are of two types, according to their generality. First, we consider the framework consisting of topological spaces without linear structure and, on the other hand, the convex case, i.e., when the range space is a vector space is separately considered. By means of one of our inverse maximum theorem, we generalize a corresponding result by Koyima. In the field of applications, we prove the equivalences of some remarkable results existing in the literature.

Some new equivalents of the Brouwer fixed point theorem

“…(XXXIV) Cortina and Fierro [6] in 2022: We deal with direct and inverse maximum theorems. Alternative versions to the Berge theorem are provided, by relaxing the compactness condition of the constraint correspondence.…”