COMPOSITE ITERATIVE METHODS FOR A GENERAL SYSTEM OF VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS (Study on Nonlinear Analysis and Convex Analysis)

Abstract

In this paper, we introduce two composite iterative methods (one implicit method and one explicit method) for finding a common element of the solution set of a general system of variational inequalities for continuous monotone mappings and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Then we establish strong convergence of the sequence generated by the proposed iterative methods to a common element of the solution set and the fixed point set, which is the unique solution of a certain variational inequality.