On multi-step iterative algorithms with inertia terms for variational inequalities and fixed point problems

In this paper, we propose a multi-step iterative algorithm for finding common solutions of pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in real Hilbert spaces. Our iterative algorithm combines self-adaptive subgradient extragradient method and inertial techniques. Strong convergence of the proposed algorithm is proved under some assumptions.