Subgradient extragradient algorithm with double inertial steps for solving variational inequality problems and fixed point problems in Hilbert spaces

In this paper, we introduce a subgradient extragradient method with double inertial extrapolation steps and self-adaptive step sizes for finding a common solution of the variational inequality problem, involving a pseudo-monotone mapping and Lipschitz continuous operator and the fixed point problem with a quasi-nonexpansive in real Hilbert spaces. Weak convergence theorems are obtained under some appropriate conditions imposed on the parameters. Numerical experiments are given to illustrate the efficiency of our proposed algorithm.