Type Volterra property in Functional Differential Equations. Study of the Cauchy problem and extremal solutions

We study a class of Functional Differential Equations whose hereditary structure is induced by a Volterra type property. This abstract formulation allows us to unify many hereditary structures already introduced in literature. For the Cauchy problem, existence, uniqueness and continuous dependence theorems are given. Moreover, existence and continuous dependence results for extremal solutions are proved.