Abstract
In this manuscript, we accelerate the modified inertial Mann-like algorithm by involving Tikhonov regularization terms. Strong convergence for fixed points of nonexpansive mappings in real Hilbert spaces was discussed utilizing the proposed algorithm. Accordingly, the strong convergence of a forward-backward algorithm involving Tikhonov regularization terms was derived, which counts as finding a solution to the monotone inclusion problem and the variational inequality problem. Ultimately, some numerical discussions are presented here to illustrate the effectiveness of our algorithm.