The paper deals with the Hyers-Ulam-Rassias stability for nonlinear Volterra equations of the form
where is a continuous function satisfying a Lipschitz condition with respect to the third variable. The integral equation (1) possesses the Hyers-Ulam-Rassias stability if for each function satisfying the condition
where is a non-negative function, there exist a solution of (1) and a constant independent of and such that
The Hyers-Ulam stability means that in (2)–(3) is a constant function.
Sufficient conditions for the Hyers-Ulam-Rassias and Hyers-Ulam stabilities of the integral equation (1) on a finite interval are established. The Hyers-Ulam-Rassias stability conditions are also obtained for the nonlinear Volterra equations of the form (1) in the case of infinite intervals.