H. A. Abass†
Abstract: In this paper, we study and introduce a self adaptive method together with a Halpern iterative algorithm for approximating solutions of multiple‑sets split monotone variational inclusion problem which includes the multiple‑sets split feasibility problem, split feasibility problem, split monotone variational inclusion problem and split variational inclusion problem, to mention a few. Using our iterative algorithm, we prove a strong convergence result for approximating the solution of the aforementioned problems. Numerical examples on finite‑dimensional and infinite‑dimensional spaces are displayed to illustrate the performance of our iterative method. The result discussed in this article extends and complements many related results in literature.
MSC: 47H09; 47H10; 47J05; 47J25.
keywords: Multiple‑sets split monotone variational problem, Halpern method, fixed point problems, Iterative method.
DOI 10.56082/annalsarscimath.2023.1-2.535
†hammedabass548@gmail.com, abassh@ukzn.ac.za, School of Mathematics, Statistics and Computer Science, University of KwaZulu‑Natal, Durban, South Africa; DSI‑NRF Center of Excellence in Mathematical and Statistical Sciences (CoE‑MaSS), Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Pretoria, South Africa.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 15 no 1-2, 2023
