Inertial Tseng Method for Solving the Variational Inequality Problem and Monotone Inclusion Problem in Real Hilbert Space

The main aim of this research is to introduce and investigate an inertial Tseng iterative method to approximate a common solution for the variational inequality problem for γ-inverse strongly monotone mapping and monotone inclusion problem in real Hilbert spaces. We establish a strong convergence theorem for our suggested iterative method to approximate a common solution for our proposed problems under some certain mild conditions. Furthermore, we deduce a consequence from the main convergence result. Finally, a numerical experiment is presented to demonstrate the effectiveness of the iterative method. The method and methodology described in this paper extend and unify previously published findings in this field.