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Author: search.filters.author.Mebawondu, Akindele AdebayoHas files: Yes

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    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, Adhir
    The 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.
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    A new relaxed Tseng method for finding a common solution of fixed point and split monotone inclusion problems
    (Kyungnam University Press, 2024-02-29) Mzimela, Lusanda; Mebawondu, Akindele Adebayo; Maharaj, Adhir; Izuchukwu, Chinedu; Narain, Ojen Kumar
    In this paper, we study the problem of nding a common solution to a xed point problem involving a nite family of -demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and e cient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.