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Author: search.filters.author.Narain, Ojen KumarSubject: search.filters.subject.Hilbert space

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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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    An inertial Tseng algorithm for solving quasimonotone variational inequality and fixed point problem in Hilbert spaces
    (Kyungnam University Press, 2024-02) Kajola, Shamsudeen Abiodun; Narain, Ojen Kumar; Maharaj, Adhir
    In this paper, we propose an inertial method for solving a common solution to fixed point and Variational Inequality Problem in Hilbert spaces. Under some standard and suitable assumptions on the control parameters, we prove that the sequence generated by the proposed algorithm converges strongly to an element in the solution set of Variational Inequality Problem associated with a quasimonotone operator which is also solution to a fixed point problem for a demimetric mapping. Finally, we give some numerical experiments for supporting our main results and also compare with some earlier announced methods in the literature.