### Asymptotic behavior in neutral difference equations with variable coefficients and more than one delay arguments

#### Abstract

In this paper, we study the asymptotic behavior of the solutions of a neutral type difference equation of the form

Δ[x(n)+∑_{j=1}^{w}q_{j}(n)x(τ_{j}(n))]+p(n)x(σ(n))=0, n≥0

where (p(n))_{n≥0} is a sequence of positive real numbers such that p(n)≥p, p∈ℝ₊, τ_{j}(n), j=1,...,w are general retarded arguments, σ(n) is a general deviated argument (retarded or advanced), (q_{j}(n))_{n≥0}, j=1,...,w are sequences of real numbers, and Δ denotes the forward difference operator Δx(n)=x(n+1)-x(n).

**How to Cite this Article:**George E Chatzarakis, G. N. Miliaras, Asymptotic behavior in neutral difference equations with variable coefficients and more than one delay arguments, Journal of Mathematical and Computational Science, Vol 1, No 1 (2011), 32-52 Copyright © 2011 George E Chatzarakis, G. N. Miliaras. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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