φ-regular functions in Asplund spaces

We introduce in the context of Asplund spaces, a new class of phi-regular functions. This new concept generalizes the one of prox-regularity introduced by Poliquin & Rockafellar (2000) in R-n and extended to Banach spaces by Bernard & Thibault (2004). In particular, the class of phi-regular functions includes all lower semi-continuous convex functions, all lower-C-2 functions, and convexly C-1,C-0-composite functions as well. Geometrical and subdifferential characterizations for this new class of functions are investigated.