A discrete Gronwall–Halanay-type inequality with infinite delay and its applications to difference equations.

We establish a discrete Gronwall–Halanay-type inequality with infinite delay, which is not covered in the existing literature. As an application, a new criterion is obtained for the asymptotic stability of the zero solutions for a class of Volterra difference equations. A concrete example is also given to illustrate the efficiency of the general results. [ABSTRACT FROM AUTHOR]