Acta mathematica scientia, Series B >
A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES
Received date: 2010-05-24
Online published: 2012-07-20
Supported by
This project was supported by the Scientific Research Fun of Sichuan Normal University (11ZDL01) and the Sichuan Province Leading Academic Discipline Project (SZD0406).
A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued map-pings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and gen-eralize some recent results in this field.
DING Xie-Ping . A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1571 -1583 . DOI: 10.1016/S0252-9602(12)60124-6
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