On a Max-Type Difference Equation

Abstract

We prove that every positive solution of the max-type difference equation xn=max⁡{A/xn-pα,B/xn-kβ}, n=0,1,2,… converges to x¯=max⁡{A1/(1+α),B1/(1+β)} where p,k are positive integers, 0<α,β<1, and 0<A,B.