Solution space characterisation of perturbed linear functional and integrodifferential Volterra convolution equations: Ces\`aro limits

In this article we discuss the requirements needed in order to characterise the solution space of perturbed linear integrodifferential Volterra convolution equations. We highlight how integrodifferential equations react far better under perturbations than their integral equation counterparts in regards to stability of solutions. To illustrate this idea we give a characterisation of when the Ces\`aro mean of solutions converge to a limit, which is explicitly identified and given in terms of the problem data. Additionally we note how all results can also be applied to functional differential equations.