Averaging of functional differential inclusions in Banach spaces

Averaging schemes for functional differential inclusions in Banach spaces with slow and fast time variables are studied. Under mild suppositions on the regularity, the periodic case and the case of non-existence of an average are investigated. The accuracy of the averaging technique is considered as well. In particular, for periodic systems, the usual linear approximation is achieved. Under stronger regularity conditions, approximation orders for Krylov-Bogoliubov-Mitropolskii type right-hand sides are derived.