A strong convergence halpern-type inertial algorithm for solving system of split variational inequalities and fixed point problems^∗

In this paper, we propose a new Halpern-type inertial extrapola-tion method for approximating common solutions of the system of split varia-tional inequalities for two inverse-strongly monotone operators, the variational inequality problem for monotone operator, and the fixed point of composi-tion of two nonlinear mappings in real Hilbert spaces. We establish that the proposed method converges strongly to an element in the solution set of the aforementioned problems under certain mild conditions. In addition, we present some numerical experiments to show the efficiency and applicability of our method in comparison with some related methods in the literature. This result improves and generalizes many recent results in this direction in the literature.