Iterative Methods for Pseudomonotone Variational Inequalities and Fixed‐Point Problems

In this paper, we introduce an iterative scheme for finding a common element of the set of solution of a pseudomonotone, Lipschitz‐continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well‐known schemes: extragradient and approximate proximal methods. We derive some necessary and sufficient conditions for strong convergence of the sequences generated by the proposed scheme.