Authors: Xie Ping Ding
Publish Date: 2011/05/17
Volume: 53, Issue: 3, Pages: 525-537
Abstract
A new class of bilevel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in Banach spaces First an auxiliary generalized mixed equilibrium problem AGMEP to compute the approximate solutions of the generalized mixed equilibrium problems GMEP and bilevel generalized mixed equilibrium problems BGMEP involving setvalued mappings is introduced By using a minimax inequality the existence and uniqueness of solutions of the AGMEP is proved under quite mild conditions By using auxiliary principle technique new iterative algorithm to compute the approximate solutions of the GMEP and the BGMEP are suggested and analyzed The strong convergence of the iterative sequences generated by the algorithms are proved under quite mild assumptions These results are new and generalize some recent results in this field
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