Asymptotic behavior of higher-order neutral difference equations with general arguments

We study the asymptotic behavior of solutions of the higher-order neutral difference equation where τ ( n ) is a general retarded argument, σ( n ) is a general deviated argument, c ∈ ; ( p ( n )) n ≥ 0 is a sequence of real numbers, ∆ denotes the forward difference operator ∆ x ( n ) = x ( n +1) - x ( n ); and ∆ j denotes the j th forward difference operator ∆ j ( x ( n ) = ∆ (∆ j -1 ( x ( n ))) for j = 2, 3,…, m . Examples illustrating the results are also given.