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Auxiliary Principle and Algorithm of Solutions for a New System of Generalized Mixed Equilibrium Problems in Banach Spaces

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  • X. P. Ding

    (Sichuan Normal University)

Abstract

In this paper, we study a new system of generalized mixed equilibrium problems involving nonmonotone set-valued mappings and nondifferential bifunctions in Banach spaces. First, a system of auxiliary generalized mixed equilibrium problems are introduced. By using a minimax inequality, the existence and uniqueness of solutions of the system of auxiliary generalized mixed equilibrium problems is proved. Next, by using the auxiliary principle technique, an iterative algorithm for solving the system of generalized mixed equilibrium problems is constructed. Finally, the existence of solutions and the convergence of iterative sequences generated by the algorithm are proved under suitable conditions. These results improve, unify, and generalize many corresponding known results given in literature.

Suggested Citation

  • X. P. Ding, 2012. "Auxiliary Principle and Algorithm of Solutions for a New System of Generalized Mixed Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 796-809, December.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:3:d:10.1007_s10957-012-0102-x
    DOI: 10.1007/s10957-012-0102-x
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    References listed on IDEAS

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    1. X. P. Ding, 2005. "Existence of Solutions and an Algorithm for Mixed Variational-Like Inequalities in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 127(2), pages 285-302, November.
    2. L. C. Zeng & S. Schaible & J. C. Yao, 2005. "Iterative Algorithm for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 725-738, March.
    3. X. P. Ding, 2010. "Auxiliary Principle and Algorithm for Mixed Equilibrium Problems and Bilevel Mixed Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 347-357, August.
    4. Q. H. Ansari & J. C. Yao, 2001. "Iterative Schemes for Solving Mixed Variational-Like Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 527-541, March.
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