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This paper investigates the common set of solutions of a variational inequality, a mixed equilibrium problem, and a hierarchical fixed-point problem in a Hilbert space. A numerical method is proposed to find the approximate element of this common set. The strong convergence of this method is proved under some conditions. The proposed method is shown to be an improvement and extension of some known results.

journal of inequalities and applications

Strong convergence algorithm for approximating the common solutions of a variational inequality, a mixed equilibrium problem and a hierarchical fixed-point problem