On evenly convex sets and functions

A subset of Rn is said to be evenly convex (e-convex, in breaf) if it isthe intersection of some family (possibly empty) of open halfspaces. In thispaper, we collect some published results which show that this large classof convex sets enjoys a lot of the well-known properties of the subclassof closed convex sets. We also consider functions whose epigraphs aree-convex sets, the so-called e-convex functions, and we show the mainproperties of this class of convex functions that contains the importantclass of lower semicontinuous convex functions

closed convex sets; evenly convex sets; lower semicontinuous; convex functions; evenly convex functions

On evenly convex sets and functions Articles