Iterative methods for pseudomonotone variational inequalities and fixed-point problems (Q1934630)

This paper presents an iterative scheme that combines two well-known schemes: extragradient and approximate proximal methods. The authors suggest an iterative scheme for finding a common element of the set of solutions of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. Some necessary and sufficient conditions are derived for strong convergence of the sequences generated by the proposed scheme. The results presented in this paper extend and improve some corresponding results in the literature.