A function defined on a locally convex space is called evenly quasiconvex if its level sets are intersections of families of open halfspaces. Furthermore, if the closures of these open halfspaces do not contain the origin, then the function is called R-evenly quasiconvex. In this note, R-evenly quasiconvex functions are characterized as those evenly-quasiconvex functions that satisfy a certain simple relation with their lower semicontinuous hulls.
- Generalized conjugation
- Quasiconvex functions