A solution of a nonlinear Volterra integral equation with delay via a faster iteration method
Godwin Amechi Okeke, Austine Efut Ofem, Thabet Abdeljawad, Manar A. Alqudah, Aziz Khan
Abstract
<abstract><p>The purpose of this article is to study the convergence, stability and data dependence results of an iterative method for contractive-like mappings. The concept of stability considered in this study is known as $ w^2 $-stability, which is larger than the simple notion of stability considered by several prominent authors. Some illustrative examples on $ w^2 $-stability of the iterative method have been presented for different choices of parameters and initial guesses. As an application of our results, we establish the existence, uniqueness and approximation results for solutions of a nonlinear Volterra integral equation with delay. Finally, we provide an illustrative example to support the application of our results. The novel results of this article extend and generalize several well known results in existing literature.</p></abstract>