A Krasnoselskii–Ishikawa Iterative Algorithm for Monotone Reich Contractions in Partially Ordered Banach Spaces with an Application

Nawab Hussain, Saud M. Alsulami and Hind Alamri
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Nawab Hussain: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Saud M. Alsulami: Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Hind Alamri: Department of Mathematics, Collage of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Mathematics, 2021, vol. 10, issue 1, 1-19

Abstract: Iterative algorithms have been utilized for the computation of approximate solutions of stationary and evolutionary problems associated with differential equations. The aim of this article is to introduce concepts of monotone Reich and Chatterjea nonexpansive mappings on partially ordered Banach spaces. We describe sufficient conditions for the existence of an approximate fixed-point sequence (AFPS) and prove certain fixed-point results using the Krasnoselskii–Ishikawa iterative algorithm. Moreover, we present some interesting examples to highlight the superiority of our results. Lastly, we provide both weak and strong convergence results for such mappings and consider an application of our results to prove the existence of a solution to an initial value problem.

Keywords: approximate fixed-point sequence; Krasnoselskii–Ishikawa iterative algorithm; ordered Reich and Chatterjea nonexpansive mappings; weak and strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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