Abstract
In this paper, several sequential formulae are obtained for the Brøndsted-Rockafellar ε-subdifferential of the sum and the composition of two convex and lower semicontinuous mappings defined in reflexive Banach spaces. These calculus rules are stated in terms of limits ofε-subgradients at nearby points to the nominal point without assuming any qualification condition, and extend some well-known sequential formulae for the Fenchel subdifferential. Next, as a consequence of these formulae, sequential sum and composition rules for a proper ε-subdifferential of extended vector mappings are obtained, which involve a type of vector strong ε-subdifferential.