Some Stability Theorems for Systems of Volterra Integral Equations

Many types of stability have been studied in the theory of ordinary differential equations. Our present purpose is to study perturbed Volterra integral equations (which are a generalization of the initial value problem for ordinary differential equations), As a natural generalization of these concepts for ordinary differential equations, we define stability, uniform stability, and asymptotic stability for integral equations and prove various theorems for linear and perturbed integral equations.