characterization of d.c. functions in terms of quasidifferentials

a characterization of d.c. functions f:ω→r in terms of the quasidifferentials of f is obtained, where ω is an open convex set in a real banach space. recall that f is called d.c. (difference of convex) if it can be represented as a difference of two finite convex functions. the relation of the obtained results with known characterizations is discussed, specifically the ones from [r. ellaia, a. hassouni, characterization of nonsmooth functions through their generalized gradients, optimization 22 (1991), 401–416] in the finite-dimensional case and [a. elhilali alaoui, caractérisation des fonctions dc, ann. sci. math. québec 20 (1996), 1–13] in the case of a banach space.