Faculty of Applied Sciences
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Item An inertial iterative method for solving split monotone inclusion problems in Hilbert spaces(American Institute of Mathematical Sciences (AIMS), 2024) Mebawondu, Akindele Adebayo; Sunday, Akunna Sunsan; Narain, Ojen Kumar; Maharaj, AdhirThe 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.