(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.
