COMPULSORY ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SYSTEM OF THREE DISCRETE EQUATIONS

This contribution is devoted to a discussion of the asymptotic behavior of solutions of systems of three difference equations. We try to connect two techniques – the so called retract type technique and Liapunov type approach. We show that under appropriate conditions containing conditions typical for the retract technique approach, and conditions typical for the Liapunov type approach, there exists at least one solution of the system considered the graph of which stays in a prescribed domain.