Generalized convexity and well-posedness in vector optimization

We introduce a class of generalized convex vector valued functions, named K-quasiconnected functions, that contains, as a special case, the classical K-quasiconvex functions. The main results concerns the well-posedness of K-quasiconnected problems: moreover, under strict K-quasiconnectedness, we obtain the well-posedness of weak solutions.