ITERATIVE ALGORITHMS FOR FAMILIES OF VARIATIONAL INEQUALITIES FIXED POINTS AND EQUILIBRIUM PROBLEMS

Abstract. We introduce an iterative algorithm for finding a com-mon element of the set of fixed points for an infinite family of nonex-pansive mappings, the set of solutions of the variational inequalities for a family of α-inverse-strongly monotone mappings and the set of solutions of a system of equilibrium problems in a Hilbert space. We prove the strong convergence of the proposed iterative algo-rithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. Moreover, we apply our result to the problem of finding a common fixed point of a family of strictly pseudocontractive mappings. 1