Global behavior of two families of nonlinear symmetric difference equations (Q1958759)

Summary: We mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in \textit{S. Stević}'s paper [Appl. Math. Comput. 216, No.~1, 179--186 (2010; Zbl 1193.39008)]. A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of \textit{M. Aloqeili} [Appl. Math. Comput. 215, No.~3, 950--953 (2009; Zbl 1177.39019)], \textit{K. S. Berenhaut} and \textit{S. Stević} [J. Math. Anal. Appl. 326, No.~2, 940--944 (2007; Zbl 1112.39002)], and \textit{M. Liao} et al. [Adv. Difference Equ. 2009, Article ID 394635 (2009; Zbl 1166.39301)].