Global stability of a max-type difference equation

摘要

We show that every positive solution to the difference equationxn=maxA1xn-p1α1,A2xn-p2α2,…,Akxn-pkαk,n∈N0,where pi,i=1,…,k are natural numbers such that 1⩽p1<⋯0,αi∈(-1,1),i=1,…,k, converges to max1⩽i⩽kAi1αi+1. This result improves and complements the main result in our recent note: S. Stević, Global stability of a difference equation with maximum, Appl. Math. Comput. 210 (2009) 525–529, since it also considers the case when αi∈(-1,0],ı=1,…,k.