Extragradient-type algorithm for a class of bilevel variational inequalities with the split common fixed-point problem constraint with multiple output sets

In this paper, we investigate the problem of solving the bilevel pseudomonotone variational inequality problem with the split common fixed-point problem with multiple output sets constraint for demicontractive mappings in real Hilbert spaces. To solve this problem, we design an extragradient-type algorithm incorporating the inertial technique with a correction term and a self-adaptive step-size strategy. The strong convergence of the iterative sequence generated by the proposed algorithm is established without prior knowledge of the norms of the given bounded linear operators. Additionally, the main result is applied to solve a bilevel split pseudomonotone variational inequality problem with a fixed-point problem constraint, and several corollaries are derived. Finally, we provide numerical examples that serve to illustrate the applicability and performance of the proposed algorithm.

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