Existence of fixed points results via new enriched type of nonexpansive maps and application to delay differential equations

Abstract

In this article, we introduce an enriched \(\omega \)-Reich–Suzuki type nonexpansive mapping and provide a couple of numerical examples to verify the existence of enriched \(\omega \)-Reich–Suzuki type nonexpansive maps. Notably, the Z-iteration method has been shown to have faster convergence rates than some well-known iteration approaches. We establish both strong and weak convergence of enriched \(\omega \)-Reich–Suzuki type nonexpansive mapping using the powerful Z-iteration technique. Also, we provide an application to approximate the solution of a delay differential equation and presenting an illustrative numerical example to validate our findings.