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

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2014年第1期2014卷 1-24页

作者： Bnouhachem, Abdellah Nanjing Univ Sch Management Sci & Engn Nanjing 210093 Jiangsu Peoples R China Ibn Zohr Univ ENSA Agadir Morocco

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.

关键词： mixed equilibrium problem variational inequality problem hierarchical fixed-point problem projection method

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A modified projection method for a common solution of a system of variational inequalities, a split equilibrium problem and a hierarchical fixed-point problem

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fixed point THEORY AND APPLICATIONS 2014年第1期2014卷 22-22页

作者： Bnouhachem, Abdellah Nanjing Univ Sch Management Sci & Engn Nanjing 210093 Jiangsu Peoples R China Ibn Zohr Univ ENSA Agadir Morocco

In this paper, we suggest and analyze a modified projection method for finding a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem in the setting of real Hilbert spaces. We prove the strong convergence of the sequence generated by the proposed method to a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem. Several special cases are also discussed. The results presented in this paper extend and improve some well-known results in the literature.

关键词： system of variational inequalities equilibrium problem hierarchical fixed-point problem fixed-point problem projection method

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