A modified Halpern-type S-iteration process for a finite family of variational inequality problems in real Hilbert space

This paper considers a finite family of variational inequality problems and fixed point problems in real Hilbert space. With the help of averaged mappings, we propose a new iterative process to solve the above-mentioned problem. Our proposed algorithm is the combination of Halpern iterative process, subgradient extragradient process and S-iteration process for variational inequalities. Under reasonable restrictions on control sequences, a strong convergence theorem has been proved. Further, some numerical experiments indicate that the suggested approach is practical.