Alternated multi-step inertial iterative algorithm for solving the split feasibility problem in Hilbert spaces

In this paper, we propose an alternated multi-step inertial iterative algorithm for solving the split feasibility problem involving two bounded linear operators in Hilbert spaces. The proposed algorithm adopts self-adaptive step size and the step size is bounded away from zero. Under some mild conditions, the strong convergence of the sequence generated by the proposed algorithm is established. Finally, the numerical experiments are presented to verify the effectiveness and superiority of our proposed algorithm. Our results are innovative and can be an enrichment to the recently published results in the literature. © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2024.