A discrete-time adaptive ILC scheme is presented for systems with time-varying parametric uncertainties. Using the analogy between the discrete-time axis and the iterative learning axis, the new AILC can incorporate a recursive Least-Squares algorithm, hence the learning gain can be tuned iteratively along the learning axis and pointwisely along the time axis. When the initial states are random...

Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E , which is also a nonexpansive retract of E with nonexpansive retraction P . Let {Ti : i ∈ I } be N nonself asymptotically nonexpansive mappings from K to E such that F = {x ∈ K : Ti x = x, i ∈ I } 6= φ, where I = {1, 2, . . . , N }. From arbitrary x0 ∈ K , {xn} is defined by xn = P((1− αn)xn−1 + αnTn(PT...

The theory of modular spaces was initiated by Nakano 1 in 1950 in connection with the theory of order spaces and redefined and generalized by Musielak and Orlicz 2 in 1959. These spaces were developed following the successful theory of Orlicz spaces, which replaces the particular, integral form of the nonlinear functional, which controls the growth of members of the space, by an abstractly give...