Abstract

The purpose of this paper is to study a class of generalized convex functions defined on a Banach space X, called approximate convex functions which are stable under finite sums and finite suprema, and for which most of the known subdifferentials such as the Clarke, the Mordukhovich and the Ioffe approximate subdifferential coincide and share several properties of the Fenchel-Moreau-Rockafeller convex subdifferential.