On some nonlocal evolution equations in Banach spaces

This note is concerned with the initial value problem for the abstractnonlocal equation where A is amaximal monotone operator from a reflexive Banach space E to itsdual E^*, while B is a nonlocal maximal monotone operator from . Under proper boundedness and coercivity assumptions on the operators, a solution is achieved by means of a discretization argument. Uniqueness and continuous dependence are also discussed and we prove some estimates for the discretization error. Finally, we deal with the approximation of linear Volterra integrodifferential operators.