Comparison theorems for the oscillation of higher order difference equations with deviating arguments

The difference equation Δαy + δp(k)f (y (g (k))) = 0, where p(k) is positive, is classified into four cases according to α is odd or even and δ is 1 or −1. In each case, we shall offer comparison theorems for the oscillation of the difference equation. Examples are also included to illustrate the importance of the results obtained.