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Abubakar Adamu,Jitsupa Deepho,Abdulkarim Hassan Ibrahim,Auwal Bala Abubakar 경남대학교 기초과학연구소 2021 Nonlinear Functional Analysis and Applications Vol.26 No.2
In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.
Abubakar Adamu,Dilber Uzun Ozsahin,Abdulkarim Hassan Ibrahim,Pongsakorn Sunthrayuth 경남대학교 기초과학연구소 2023 Nonlinear Functional Analysis and Applications Vol.28 No.4
In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established.