Double inertial extragradient method with double projection for solving variational inequality and fixed point problems

The aim of this paper is to study a double inertial extragradient algorithm with double projection and prove a weak convergence theorem for finding a common solution of a variational inequality problem and a fixed point problem in a real Hilbert space. Furthermore, a strong convergence theorem of the proposed algorithm is established under very mild conditions. Finally, we give a numerical example to illustrate the feasibility and effectiveness of our algorithm.