We investigate the asymptotic behavior of nonautonomous discrete dynamical systems governed by the system of difference equations (recursive equations): y j ( n + 1 ) = F j ( n , y ( n ) ) ; j = 1 , … , k , n = 0 , 1 , 2 , … , where y ( n ) = ( y 1 ( n ) , … , y k ( n ) ) ∈ ℝ k , y ( 0 ) = x , and F j ( n , ⋅ ) is a mean of k  ( ≥ 2 ) positive real numbers, that is, a real-valued function satisfying the internality property min ( x ) ≤ F j ( n , x ) ≤ max ( x ) .