On approximate solutions of the generalized Volterra integral equation

We prove some results on approximate solutions of the generalized Volterra integral equation ψ(x)=∫axN(x,t,ψ(α(x,t)))dt+G(x) for continuous functions mapping a real interval II, of the form [a,b)[a,b) or [a,b][a,b] or [a,∞)[a,∞), into a Banach space. We show that, under suitable assumptions, they generate exact solutions of the equation. In particular, we consider the issue of uniqueness of approximate and exact solutions of the equation.