Characterization of d.c. functions in terms of quasidifferentials

A characterization of d.c. functions f:Ω→Rf:Ω→R in terms of the quasidifferentials of ff is obtained, where ΩΩ is an open convex set in a real Banach space. Recall that ff 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.