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Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium

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Abstract

A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem (AMEP) is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems (SGEP) is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.

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Authors and Affiliations

  1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, 610066, P. R. China

    Xie-ping Ding  (丁协平)

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  1. Xie-ping Ding  (丁协平)
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Correspondence to Xie-ping Ding  (丁协平).

Additional information

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

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Ding, Xp. Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium. Appl. Math. Mech.-Engl. Ed. 34, 113–126 (2013). https://doi.org/10.1007/s10483-013-1657-x

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  • DOI: https://doi.org/10.1007/s10483-013-1657-x

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

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