By using topological methods, expressed in terms of the Kuratowski measure of noncompactness, the authors prove several existence results on mild solutions for the infinite delay functional-integral equation
and semilinear functional-differential equations of the form
with . Here, is an admissible function space, i.e., a suitable chosen subspace of functions from to , with a Banach space, , , is either in or in and is a linear operator. An extension to the case when may depend on as well is considered, and an application to a functional integro-differential equation of Schrödinger type is included.