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 α-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.