On the classes of higher-order Jensen-convex functions and Wright-convex functions

The classes of n-Wright-convex functions and n-Jensen-convex functions are compared with each other. It is shown that for any odd natural number $n$ the first one is the proper subclass of the second one. To reach this aim new tools connected with measure theory are developed

Bernstein-Doetsch type theorems with Tabor type error terms for set-valued maps

K

Remars on K-midconvex set-valued functions with closed epigraph

In this note we present some continuity results on K-midconvex set-valued functions. In particular, we give conditions under which K-midconvex and set valued functions with closed epigraph are K-continuous