Convergence and Divergence of the Solutions of a Neutral Difference Equation

We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form Δ[()+(())]+()(())=0, where () is a general retarded argument, () is a general deviated argument (retarded or advanced), ∈ℝ, (())≥0 is a sequence of positive real numbers such that ()≥, ∈ℝ+, and Δ denotes the forward difference operator Δ()=(+1)−(). Also, we examine the asymptotic behavior of the solutions in case they are continuous and differentiable with respect to