Monotone α-nonexpansive mapping in ordered Banach space by AU-iteration algorithm with application to delay differential equation

In this paper, we adopt the AU-iteration scheme introduced by Udofia et. al. [25] (U. E. Udofia, A. E. Ofem, and D. I. Igbokwe, Convergence Analysis for a New Faster Four Steps Iterative Algorithm with an Application, Open J. Math. Anal. 5 (2021), no. 2, 95-112) to approximate the fixed point of monotone alpha-nonexpansive mappings in ordered Banach space. Analytically and with a numerical example we show that this iteration process converges faster than some well known existing iteration processes in literature. Further, we apply the AU-iteration process to find the unique solutions of a delayed differential equation.