Maximal elements and equilibria of generalized games for -majorized and condensing correspondences.
Metrization of Compact Convex Sets.
m-families and Common Transversals
Minimal pairs of bounded closed convex sets
The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.
Minimal pairs of compact convex sets
Pairs of compact convex sets naturally arise in quasidifferential calculus as sub- and superdifferentials of a quasidifferentiable function (see Dem86). Since the sub- and superdifferentials are not uniquely determined, minimal representations are of special importance. In this paper we give a survey on some recent results on minimal pairs of closed bounded convex sets in a topological vector space (see PALURB). Particular attention is paid to the problem of characterizing minimal representatives...
Minimal pairs representing selections of four linear functions in .
Minimality in asymmetry classes
We examine minimality in asymmetry classes of convex compact sets with respect to inclusion. We prove that each class has a minimal element. Moreover, we show there is a connection between asymmetry classes and the Rådström-Hörmander lattice. This is used to present an alternative solution to the problem of minimality posed by G. Ewald and G. C. Shephard in [4].
Minimax equalities by reconstruction of polytopes.
Minimax inequality of Ky Fan type in -spaces with applications.
More on exposed points and extremal points of convex sets in and Hilbert space
Let be a separable real Hilbert space, with , and let be convex and closed in . Let be a collection of linear -subspaces of . A point is called exposed by if there is a so that . We show that, under some natural conditions, can be reconstituted as the convex hull of the closure of all its exposed by points whenever is dense and . In addition, we discuss the question when the set of exposed by some points forms a -set.