Extragradient Algorithms for Solving Certain Nonlinear Problems with Application to Image Restorations

In this paper, we introduced an inertial extragradient algorithm to approximate the common solution of split fixed point, split variational inclusion and split equilibrium problems involving nonexpansive mappings and pseudomonotone Lipschitz-type bifunctions in Hilbert spaces. Moreover, using some assumptions on the control parameters, we prove the strong convergence of the proposed algorithm and then apply our main result to solve the split minimization, split feasibility and split variational inequality problems. We also present some numerical examples to show the effectiveness and applicability of the proposed scheme. We include tables illustrating the number of iterations, the CPU time for convergence, comparisons among different algorithms, and the error analysis. We apply our proposed scheme to solve the image restoration problem as another application of the result presented herein.