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Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces

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Abstract

A new system of generalized mixed equilibrium problems (SGMEPs) involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems (SAGMEPs) for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, 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).

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Contributed by Xie-ping DING

Project supported by the Scientific Research Fund of Sichuan Normal University (No. 09ZDL04) and the Sichuan Province Leading Academic Discipline Project (No. SZD0406)

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Ding, Xp. Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces. Appl. Math. Mech.-Engl. Ed. 32, 231–240 (2011). https://doi.org/10.1007/s10483-011-1409-9

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  • DOI: https://doi.org/10.1007/s10483-011-1409-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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