On the Global Attractivity of a Max-Type Difference Equation

الملخص EN

We investigate asymptotic behavior and periodic nature of positive solutions of the difference equation xn=max{A/xn−1,1/xn−3α},n=0,1,…, where A>0 and 0<α<1.

We prove that every positive solution of this difference equation approaches x¯=1 or is eventually periodic with period 2.