Global stability of a rational symmetric difference equation

Motivated by ideas from papers: C. Cinar, I. Yalcinkaya, S. Stevic, A note on global asymptotic stability of a family of rational equations, Rostock. Math. Kolloq. 59 (2004), 41-49, and S. Stevic, Global stability and asymptotics of some classes of rational difference equations, J. Math. Anal. Appl. 316 (2006), 60-68, here we confirm a conjecture on a rational symmetric difference equation from the paper: K. Berenhaut, J. Foley, S. Stevic, The global attractivity of the rational difference equation y"n=y"n"-"k+y"n"-"m1+y"n"-"ky"n"-"m, Appl. Math. Lett. 20 (2007), 54-58.