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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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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.

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Acknowledgements

Project supported by the Scientific Research Fun of Sichuan Normal University (No. 11ZDL01) and the Sichuan Province Leading Academic Discipline Project (No. SZD0406).

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Authors and Affiliations

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, 610068, China

    X. P. Ding

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  1. X. P. Ding
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Correspondence to X. P. Ding.

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Communicated by Jen-Chih Yao.

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Ding, X.P. Auxiliary Principle and Algorithm of Solutions for a New System of Generalized Mixed Equilibrium Problems in Banach Spaces. J Optim Theory Appl 155, 796–809 (2012). https://doi.org/10.1007/s10957-012-0102-x

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