Quasiconvex Linear Perturbations and Convexity

AbstractIt is known that a function fdefined on a convex subset of a vector space is convex provided that all its perturbations f+ u*by linear forms are quasiconvex. We show that, under more restrictive assumptions, the convexity of ffollows from the quasiconvexity of perturbations by just a suitable one-parameter family of linear forms.