In this article, we investigate the boundedness property of the solutions of linear
and nonlinear discrete Volterra equations in both convolution and non-convolution case.
Strong interest in these kind of discrete equations is motivated as because they represent a
discrete analogue of some integral equations. The most important result of this article is a
simple new criterion, which unifies and extends several earlier results in both discrete and
continuous cases. Examples are also given to illustrate our main theorem.