Co-radiant set-valued mappings

TL;DR

This paper introduces the concept of co-radiantness for set-valued mappings between nonnegative orthants, analyzing their structure through convexity and providing representations of increasing co-radiant mappings with closed normal values.

Contribution

It presents a novel notion of co-radiantness for set-valued mappings and offers a representation framework using intersections of graphs for these mappings.

Findings

Characterization of co-radiant set-valued mappings

Representation of increasing co-radiant mappings with closed normal values

Analysis from an abstract convexity perspective

Abstract

We introduce and study a notion of co-radiantness for set-valued mappings between nonnegative orthants of Euclidean spaces. We analyze them from an abstract convexity perspective. Our main results consist in representations, in terms of intersections of graphs, of the increasing co-radiant mappings that take closed normal values, by means of elementary members in the class of such mappings.