On positive solutions of a reciprocal difference equation with minimum

Abstract

In this paper we consider positive solutions of the following difference equation xn+1 = min {A/xn, B/xn-2}, A, B > 0. We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the difference equation xn+1 = min {A/xnxn-1...x n-k, B/xn-(k+2)....xn-(2k+2)}, A, B > 0.