Bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems in reflexive Banach spaces |
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Authors: | Xie-ping Ding |
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Affiliation: | College of Mathematics and Software Science,Sichuan Normal University,Chengdu 610066, P. R. China |
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Abstract: | A new bilevel generalized mixed equilibrium problem (BGMEP) involving generalized mixed variational-like inequality problems
(GMVLIPs) is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem
(AGMEP) is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality,
the existence and the uniqueness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions.
By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate
solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown
under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field. |
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Keywords: | bilevel generalized mixed equilibrium problem (BGMEP) generalized mixed variational-like inequality problem (GMVLIP) auxiliary principle iterative algorithm reflexive Banach space |
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