Mebawondu, Akindele AdebayoSunday, Akunna SunsanNarain, Ojen KumarMaharaj, Adhir2024-08-282024-08-282024Mebawondu, A.A. et al. 2024. An inertial iterative method for solving split monotone inclusion problems in Hilbert spaces. Numerical Algebra, Control and Optimization: 1-19. doi:10.3934/naco.20240392155-32892155-3297 (Online)https://hdl.handle.net/10321/5438The purpose of this work is to introduce and study a new type of a relaxed extrapolation iterative method for approximating the solution of a split monotone inclusion problem in the framework of Hilbert spaces. More so, we establish a strong convergence theorem of the proposed iterative method under the assumption that the set-valued operator is maximal monotone and the single-valued operator is Lipschitz continuous monotone which is weaker assumption unlike other methods in which the single-valued is inverse strongly monotone. We emphasize that the value of the Lipschitz constant is not re- quired for the iterative technique to be implemented, and during computation, the Lipschitz continuity was not used. Lastly, we present an application and also some numerical experiments to show the e ciency and the applicability of our proposed iterative method.19 penHilbert Spaces0102 Applied Mathematics0103 Numerical and Computational Mathematics4901 Applied mathematicsIterative methodSplit monotone inclusion problemHilbert spaceLipschitzArticle2024-08-2710.3934/naco.2024039