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.
