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

	Monotone $\alpha$-nonexpansive mapping in ordered Banach space by AU-iteration algorithm with application to delay differential equation
International Journal of Nonlinear Analysis and Applications
مقاله 59، دوره 13، شماره 2، مهر 2022، صفحه 673-690 اصل مقاله (534.39 K)
نوع مقاله: Review articles
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.22820.2417
نویسندگان
Unwana Udofia^* ؛ Donatus Igbokwe
Department of Mathematics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
چکیده
In this paper, we adopt the AU-iteration scheme introduced by Udofia et. al. [21] (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 delay differential equation.
کلیدواژه‌ها
Monotone؛ α-Nonexpansive mappings؛ Ordered Banach Space؛ Fixed point؛ Contraction map؛ Delay Differential Equation
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