COMPOSITE ITERATIVE METHODS FOR A GENERAL SYSTEM OF VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS

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

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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.

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