On Ulam stabilities of iterative Fredholm and Volterra integral equations with multiple time-varying delays

Abstract

In present study, we deal with nonlinear iterative Fredholm and Volterra integral equations (Fredholm and Volterra IEs) including variable time delays. We are interested here in the investigations of the uniqueness of solutions and Ulam type stabilities of that the iterative Fredholm and the Volterra IEs. The proofs of the new outcomes of the study with regard to these concepts are done in the light of the Banach fixed point theorem (Banach FPT) and the Bielecki metric. As for new contributions of the present study, here, first time we develop the relative outcomes that can be found in the literature to certain nonlinear iterative Fredholm and Volterra IEs including several variable time delays. Finally, a concrete example is introduced at the end of the study.