Weighted Norms In Advanced Volterra Difference Equations

In this research we explore the existence of bounded solutions, and periodic solutions of Advanced type Volterra difference equations of the form $$\begin{aligned} x(n) = f(n, x(n), x(n -h)) -\sum ^{\infty }_{s=n}Q(s,x(s), x(s-h))C(n-s) + p(n) \end{aligned}$$ using weighted norms and the contraction mapping principle in a suitable space. The suitable space will be constructed based on the magnitude and properties of p and the convergence properties of the term C.