An iterative method for solving split variational inclusion problem and variational inequality problem constrained by a common fixed point problem

In this paper, combining double inertial technique and viscosity technique, we construct a new iterative algorithm for finding the common solution of split variational inclusion problem and pseudomonotone variational inequality problem constrained by a common fixed point problem involving two demimetric operators in real Hilbert spaces. The strong convergence of the sequences generated by the proposed algorithm is proved under some mild assumptions. Finally, we apply our results to study other two optimization problems and we present two numerical experiments with graphical illustrations to demonstrate the efficiency of our method in comparison with some of the existing methods.