Continuous dependence on parameters of solutions to Volterra's equations

The definition of a Volterra operator on a system of equivalence relations is presented. For an appropriately selected system of relations this yields the well-known definitions treating the evolution property, the causality of operators, including Tychonoff's classical definition. The existence, the uniqueness, the extendability of local solutions to non-linear equations with Volterra operators are considered, estimates of the domains of definition of solutions are obtained, and theorems on the continuous dependence of solutions on the parameters are proved. The results so obtained are applied to the analysis of the well-posedness and to the approximate solution of the Cauchy problem for functional differential equations.