Strong quasi-continuity of set-valued functions

Discrete Set-Valued Continuity and Interpolation

The main question of this talk is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process in the same way maxima and minima, faces quite a number of theoretical difficulties that we propose to so...

Characterization of (quasi)convex Set-valued Maps

The aim of this paper is to characterize in terms of classical (quasi)convexity of extended real-valued functions the set-valued maps which are K-(quasi)convex with respect to a convex cone K. In particular, we recover some known characterizations of K-(quasi)convex vector-valued functions, given by means of the polar cone of K.

Monotone set-valued functions defined by set-valued Choquet integrals

In this paper, some properties of the monotone set-valued function defined by the set-valued Choquet integral are discussed. It is shown that several important structural characteristics of the original set function, such as null-additivity, strong order continuity, property(S) and pseudometric generating property, etc., are preserved by the new set-valued function. It is also shown that integr...

Parametric Set-Valued Vector Quasi-Equilibrium Problems

Continuity Properties of Convex-type Set-valued Maps

K–convex, K–midconvex and (K,λ)–convex set–valued maps are considered. Several conditions implying the continuity of such maps are collected.