New strong convergence analysis for variational inequalities and fixed point problems

In this paper, we obtain strong convergence results for solving variational inequality and fixed point problems using a combination of the Forward-Backward-Forward method and the Krasnoselkii–Mann iteration method with an inertial extrapolation step without assuming on-line rule of the inertial parameters and the iterates. Our results present a new way of choosing inertial parameters for strongly convergent algorithms to solve variational inequality and fixed point problems different from what is obtainable in the literature whereby on-line rule is assumed. We perform numerical tests to validate our theoretical analysis.