Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, Beograd 11000, Serbia
Copyright © 2007 Bratislav D. Iričanin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a given function, where is (bounded or unbounded) subinterval of ,
and . Assume that if ,
if , and is non- decreasing in the last variable .
We then prove that every bounded solution of an autonomous
difference equation of order , namely, , with initial values , is convergent, and every unbounded solution tends either to or to .