The authors derive asymptotic stability results for solutions of delay functional integro-differential equations of the type
The idea is based on an approach introduced by M. Zennaro [Numer. Math. 77, 549–563 (1997; Zbl 0886.65092)] who studied stability with resprect to the forcing term. Therefore, the initial integro-differential equation is reformulated into
using the delay Volterra integral operator
Studying stability and contractivity properties of the latter equation allows to deduce similar properties for solutions generated by continuous Runge-Kutta or collocation methods.