| Abstract | We deal with generalized notions of convexity for sets. Namely, the polyconvexity, quasiconvexity, rank one convexity and separate convexity. The question has its origin in the calculus of variations. We try to systematize the results concerning these generalized notions imitating as much as possible the classical approach of convex analysis. Throughout the article, we will discuss the relations between the different convexities, separation and Carathéodory type theorems, the notion of hull of a set and extremal points. |
