Wiener–Hopf equation technique for variational inequalities and nonexpansive mappings

In this paper, we introduce and consider a new class of Wiener–Hopf equations involving the nonlinear operator and nonexpansive operators. Essentially using the projection technique we establish the equivalence between the Wiener–Hopf equations and variational inequalities. Using this alternative equivalent formulation, we suggest and analyze an iterative method for finding the common element of the set of fixed points of nonexpansive mappings and the set of solutions of the variational inequalities. We also study the convergence criteria of iterative methods under some mild conditions. Our results include the previous results as special cases and may be considered as an improvement and refinement of the previously known results.