Characterizing set-valued evenly convex functions

M. D. Fajardo Gomez

In this work we deal with set-valued functions with values in the power set of a separated locally convex space where a nontrivial pointed convex cone induces a partial order relation. A set-valued function is evenly convex if its epigraph is an evenly convex set, i.e., it is the intersection of an arbitrary family of open half-spaces. We characterize evenly convex set-valued functions as the pointwise supremum of its set-valued e-affine minorants.

Palabras clave: Evenly convex sets set-valued functions partially ordered spaces

A. Hantoute

A. Mus, I. Martí-Vidal

T. H. Bui