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Abubakar Adamu,Dilber Uzun Ozsahin,Abdulkarim Hassan Ibrahim,Pongsakorn Sunthrayuth 경남대학교 수학교육과 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.