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In this paper, we introduce two kinds of iterative methods for finding the minimum-norm solution to the standard monotone variational inequality problems in a real Hilbert space. We then prove that the proposed iterative methods converge strongly to the minimum-norm solution of the variational inequality. Finally, we apply our results to the constrained minimization problem and the split feasibility problem as well as the minimum-norm fixed point problem for pseudocontractive mappings.

Iterative methods for finding the minimum-norm solution of the standard monotone variational inequality problems with applications in Hilbert spaces