Hull-concave set-valued functions - Fiacca, Antonella; Nikodem, Kazimierz; Papalini, Francesca (Annales Mathematicae Silesianae, 1994)
A set-valued function F is called hull-concave if F(tx + (1-t)y) ⊂ co(tF(x) + (1-t)F(y)) for all x,y from the domain of F and all t∈[0,1]. It is shown that if a hull-concave set-valued function F is defined on an open convex subset D of ℝn and for every x∈D the set clF(x) is convex and bounded, then F is continuous on D. Some other properties of hull-concave set-valued functions are also given.