and Applied Analysis 3 is a helpful tool in the analysis of solutions of 1.1 . Let v ∈ Zn0 . The function ω : Tv−k → R is said to be a solution of 2.1 on Tv−k if ω satisfies 2.1 for n ∈ Zv . A solution ω of 2.1 on Tv−k is asymptotically convergent if the limit limn→∞ω tn exists and is finite. We give some properties of solutions of inequalities of type 2.1… (More)