Asymptotic behaviour of periodic solutions in Banach space (Q1110797)

Let \(\{C_ t\}_{t\geq 0}\) be a nonempty closed convex subset of a Banach space X and U(t,s) (0\(\leq s\leq t)\) be a nonexpansive operaor constrained in \(\{C_ t\}\). A function u(t) is an almost semitrajectory of U(t,s) if \(\lim_{s\to \infty}\sup_{t\geq s}| u(t)- U(t,s)u(s)| =0.\) This paper is concerned with the asymptotic behavior of the T-periodic integral solution of \[ \frac{du}{dt}+Au(t)\to f(t),\quad u(0)=x, \] where A is an m-accretive operator.