Asymptotic properties for a class of difference inclusions associated with iterated function systems

This paper is concerned with a class of difference inclusions of the form $x(t+1)\in f(x(t))$, $t \in [0, \infty )$, each with initial data defined on a given bounded interval, and the set-valued function on the right-hand side is induced by an iterated function system (IFS). We prove that the initial data considered for difference inclusions generated by non-overlapping IFS do not affect the asymptotic behaviour of their solutions.