Approximate controllability of nonlinear discrete systems in Banach spaces (Q912036)

Using essentially methods of stability theory we present new sufficient conditions for the global approximate controllability of nonlinear discrete-time systems with rather general constrained controls in infinite-dimensional spaces. We shall also point out a class of nonlinear discrete-time systems which are not globally approximately controllable. The results of this note extend the corresponding results of \textit{A. P. Marinich} [Differ. Equations 20, 313-316 (1984); translation from Differ. Uravn. 20, No.3, 413-417 (1984; Zbl 0543.93006)] and the author [Math. Operationsforsch. Stat., Ser. Optimization 14, 371-375 (1983; Zbl 0544.93007)].