In this paper, we suggest and analysis a viscosity iterative algorithm for finding a common element of the set of solution of a mixed equilibrium problem and the set the of solutions of a variational inequality and all common fixed points of a nonexpansive semigroup. This algorithm strongly converges to an element which solves an optimization problem system. Finally, some examples and numerical results are also given.

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In this paper, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem system (GEPS) and the set of fixed points of a nonexpansive semigroup. Furthermore, we present some numerical examples (by using MATLAB software) to guarantee the main result of this paper.

Abstract.We suggest an explicit viscosity iterative algorithm for finding a common element of the set of solutions for an general equilibrium problem system (GEPS) involving a bifunction defined on a closed, convex subset and the set of fixed points of a nonexpansive semigroup on another one in Hilbert's spaces. Furthermore, we present some numerical examples(by using MATLAB software) to guarantee the main result of this paper.