Inertial iterative method for solving variational inequality problems of pseudo-monotone operators and fixed point problems of nonexpansive mappings in Hilbert spaces

Abstract

<p style='text-indent:20px;'>In this paper, we propose a new inertial viscosity iterative algorithm for solving the variational inequality problem with a pseudo-monotone operator and the fixed point problem involving a nonexpansive mapping in real Hilbert spaces. The advantage of the proposed algorithm is that it can work without the prior knowledge of the Lipschitz constant of the mapping. The strong convergence of the sequence generated by the proposed algorithm is proved under some suitable assumptions imposed on the parameters. Some numerical experiments are given to support our main results.</p>