Global behavior of two higher-order symmetric difference equations

Abstract

Motivated by papers [3, 5] here we investigate the global asymptotic stability for positive solutions of the symmetric difference equation y_n = (y_n-k^r-ky_n-l^r-ly_n-m^r + y_n-k^r + y_n-l^r + y_n-m^r)/(y_n-k^ry_n-l^r + y_n-k^r - ky_n-m^r + y_n-l^r-ly_n-m^r+ 1), where 1 ≤ k < l < m and r ε (0,1], as well as of the somewhat simpler one y_n = (y_n-k^r + y_n-l^r)/(1 + y_n-k^r - ky_n-l^r), ^where 1 ≤ k < l and r ε (0, 1]. Our main results extend the main results in [3, 5], where the cases when r = 1 were studied.