Discrete approximations and fixed set iterations in Banach spaces

We study autonomous differential inclusions with right-hand sides satisfying a onesided Lipschitz (OSL) condition in Banach spaces with uniformly convex duals. We first show that the solution set is closed and obtain estimates for Euler-type discrete approximations. We then use these results to derive an analogue of the exponential formula for the reachable set, as well as results regarding the existence and approximation of a strongly invariant attractor in the case of a negative OSL constant. As a by-product, conditions for controllability of the reverse-time system are obtained.