On a max-type and a min-type difference equation

摘要

This note shows that every positive solution to the following third order non–autonomous max-type difference equationxn+1=maxAnxn,xn-2,n∈N0,when (An)n∈N0 is a three-periodic sequence of positive numbers, is periodic with period three. The same result was proved for the following min-type difference equationxn+1=minAnxn,xn-2,n∈N0.