On the asymptotic stability of xn+1=(a+xnxn−k)/(xn+xn−k)xn+1=(a+xnxn−k)/(xn+xn−k)

We prove that the equilibrium solution of the rational difference equation xn+1=a+xnxn−kxn+xn−k,n=0,1,2,… where kk is a nonnegative integer, a≥0a≥0, and x−k,…,x0>0x−k,…,x0>0, is globally asymptotically stable.