ABSTRACT
Abstract Halanay's inequality provides a decreasing bound on a function satisfying a delay-differential inequality, subject to certain conditions, and it has been used by Halanay to analyze asymptotic stability of the zero solution of a certain delay-differential equations with fixed lag. The original inequality can be extended to allow discussion of the stability of solutions of Volterra functional equations of a more general type. Analogous theories can be obtained for discretized versions of these functional equations, using discrete Halanay-type inequalities. The purpose of this paper is to give generalized Halanay inequalities, and to indicate their use.
