Convergence and Divergence of the Solutions of a Neutral Difference Equation

Abstract

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