Asymptotic stability and boundedness criteria for nonlinear retarded Volterra integro-differential equations

In this article, we construct new specific conditions for the asymptotic stability (AS) and boundedness (B) of solutions to nonlinear Volterra integro-differential equations (VIDEs) of first order with a constant retardation. Our analysis is based on the successful construction of suitable Lyapunov-Krasovskii functionals (LKFs). The results of this paper are new, and they improve and complete that can be found in the literature.