GLOBAL ASYMPTOTIC STABILITY FOR GENERAL SYMMETRIC RATIONAL DIFFERENCE EQUATIONS.

We investigate the global asymptotic stability for positive solutions to a class of general symmetric rational difference equations and prove that the unique positive equilibrium 1 of the general symmetric rational difference equations is globally asymptotically stable. As a special case of our result, we solve the conjecture raised by Berenhaut, Foley and Stević ['The global attractivity of the rational difference equation yn = (yn-k+yn-m)/(1+yn-kyn-m)', Appl. Math. Lett. 20 (2007), 54-58]. [ABSTRACT FROM AUTHOR]