IMPLICIT WIENER-HOPF EQUATIONS AND QUASI VARIATIONAL INEQUALITIES

Abstract

In this paper, we introduce and consider a new class of Wiener-Hopf equations involving the nonlinear operator and nonexpansive operators, which is called the implicit Wiener-Hopf equations. Essentially using the projection technique, we establish the equivalence between the implicit Wiener-Hopf equations and quasi 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 quasi 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.