On the difference equation zm+1 = f(zm, zm-1, …, zm–k)

In the present work, we investigate the stability, periodicity and oscillation of the solution for a new general class of difference equations. Actually, this is the most general form of linear difference equations. Hence, the results in this article apply to several other equations that are special cases of the proposed equation. We also use an efficient method to study periodic solution of period two, with no restriction of the coefficients of difference equations, i.e. they are arbitrary real numbers. Finally, we give three applications of these equations to support our analysis