Solving Variational Inequalities Related to the Split Common Fixed Point Problem with Multiple Output Sets Constraints

In this paper, we explore the task of addressing strongly monotone variational inequalities over the solution set of the split common fixed point problem with multiple output sets in real Hilbert spaces. We propose a new iterative algorithm designed specifically for this task, which incorporates dynamic step sizes that adapt based on information from previous iterations. This approach ensures strong convergence without the need for prior knowledge of the norm of the bounded linear operator involved. Additionally, our method does not require information about the Lipschitz constants or the strongly monotone constants of the mappings. We also present several corollaries derived from our main result. Finally, we present an application of the split common fixed point problem with multiple output sets to supply chain planning, and provide numerical experiments to evaluate the performance of the proposed algorithm in comparison with existing methods.